Question 1

Find the probability. Round to the nearest ten-thousandth when necessary.
-A fair coin is tossed 5 times. What is the probability of no heads?
A) 0.0625
B) 0.9688
C) 0
D) 0.0313

Accepted Answer

The probability of getting no heads (all tails) in 5 tosses of a fair coin is (1/2)^5 = 0.03125, which rounds to 0.0313.

Question 2

Find the probability. Round to the nearest ten-thousandth when necessary.
-A coin is biased to show 43% heads and 57% tails. The coin is tossed twice. What is the probability That the coin turns up heads on the second toss?
A) 0.1849
B) 0.43
C) 0.2451
D) 0.57

Accepted Answer

The probability that the coin turns up heads on the second toss is independent of the first toss, so it remains 43% or 0.43.

Question 3

Find the probability. Round to the nearest ten-thousandth when necessary.
-A fair coin is tossed 5 times. What is the probability of exactly 3 head(s)?
A) 0.0625
B) 0.0313
C) 0.125
D) 0.3125

Accepted Answer

The probability of getting exactly 3 heads in 5 tosses of a fair coin can be calculated using the binomial probability formula, which is P(X=k) = (n choose k) * p^k * (1-p)^(n-k), where n is the number of trials, k is the number of successful outcomes, and p is the probability of success on a single trial. For this scenario, n=5, k=3, and p=0.5 (since it's a fair coin). Thus, P(3 heads) = (5 choose 3) * (0.5)^3 * (0.5)^(5-3) = 10 * 0.125 * 0.25 = 0.3125.

Question 4

Find the probability.
-What is the probability that 8 rolls of a fair die will show three threes? Round to the nearest Ten-thousandth.
A) 0.1042
B) 0.0208
C) 0.2084
D) 0.0521

Accepted Answer

The probability of rolling three threes in 8 rolls of a fair die can be calculated using the binomial probability formula: P(X=k) = (n choose k) * p^k * (1-p)^(n-k), where n=8 (number of trials), k=3 (number of successes), p=1/6 (probability of rolling a three), and (1-p)=5/6 (probability of not rolling a three). Plugging these values into the formula gives P(X=3) ≈ 0.1042.

Question 5

Find the probability.
-A child rolls a 6-sided die 6 times. What is the probability of the child rolling exactly two fours? Round to the nearest ten-thousandth.
A) 0.2009
B) 0.0621
C) 0.5681
D) 0.7182

Accepted Answer

The probability of rolling a four on a six-sided die is 1/6. The probability of rolling two fours in six rolls is (1/6)^2 * (5/6)^4 = 0.2009 (rounded to the nearest ten-thousandth).

Question 6

Find the probability.
-A die is rolled 20 times and the number of twos that come up is tallied. Find the probability of Getting more than three twos. Round to the nearest thousandth when necessary.
A) 0.564
B) 0.433
C) 0.905
D) 0.403

Accepted Answer

The answer of Find the probability.
-A die is rolled 20 times and...

Question 7

Find the probability.
-A child rolls a 6-sided die 6 times. What is the probability of the child rolling exactly four fives? Round to the nearest ten-thousandth.
A) 0.5360
B) 0.0080
C) 0.3125
D) 0.9688

Accepted Answer

The probability of rolling exactly four fives in six rolls of a 6-sided die can be calculated using the binomial probability formula, which is $P(X=k) = \binom{n}{k}p^k(1-p)^{n-k}$, where $n$ is the number of trials, $k$ is the number of successful outcomes, $p$ is the probability of success on a single trial, and $\binom{n}{k}$ is the binomial coefficient. Here, $n=6$, $k=4$, and $p=\frac{1}{6}$ (since there's one five on a 6-sided die). Plugging these values into the formula gives a probability of approximately 0.0080.

Question 8

Find the probability. Round to the nearest ten-thousandth when necessary.
-A coin is biased to show 45% heads and 55% tails. The coin is tossed twice. What is the probability That the coin turns up heads once and tails once?
A) 0.45
B) 0.55
C) 0.495
D) 0.2475

Accepted Answer

The probability of getting heads once and tails once in two tosses can be calculated by considering the two possible sequences: HT and TH. The probability for each sequence is (0.45 * 0.55) = 0.2475. Since there are two such sequences, the total probability is 2 * 0.2475 = 0.495.

Question 9

Find the probability.
-A die is rolled 20 times and the number of twos that come up is tallied. Find the probability of Getting exactly five twos. Round to the nearest thousandth when necessary.
A) 0.003
B) 0.921
C) 0.083
D) 0.129

Accepted Answer

The probability of rolling a two on a single die is 1/6. Using the binomial probability formula for 20 trials and 5 successes, the probability is approximately 0.129.

Question 10

Find the probability.
-A child rolls a 6-sided die 6 times. What is the probability of the child rolling exactly three sixes? Round to the nearest ten-thousandth.
A) 0.0536
B) 0.5362
C) 0.4441
D) 0.0594

Accepted Answer

The probability of rolling a six on a 6-sided die is 1/6. Using the binomial probability formula for exactly three successes (rolling a six) in six trials, we calculate: P(X=3) = (6 choose 3) * (1/6)^3 * (5/6)^3 ≈ 0.0536.

Question 11

Find the probability.
-A die is rolled 20 times and the number of twos that come up is tallied. Find the probability of Getting exactly two twos. Round to the nearest thousandth when necessary.
A) 0.116
B) 0.159
C) 0.198
D) 0.011

Accepted Answer

The answer of Find the probability.
-A die is rolled 20 times and...

Question 12

Find the probability.
-In a certain college, 33% of the physics majors are ethnic minorities. A random sample of 10 Physics majors is chosen. Find the probability that exactly 2 are ethnic minorities. Round to the Nearest ten-thousandth.
A) 0.0028
B) 0.1990
C) 0.2156
D) 0.1929

Accepted Answer

This problem can be solved using the binomial probability formula, which is P(X = k) = (n choose k) * p^k * (1-p)^(n-k), where n is the number of trials, k is the number of successful trials, p is the probability of success on a single trial, and (n choose k) is the binomial coefficient. Here, n=10 (the sample size), k=2 (the number of ethnic minorities we're looking for), and p=0.33 (the probability of picking an ethnic minority). Plugging these values into the formula gives us the probability of exactly 2 ethnic minorities in a sample of 10 Physics majors, which rounds to 0.1990.

Question 13

Find the probability. Round to the nearest ten-thousandth when necessary.
-What is the probability that 15 tosses of a fair coin will show 5 tails?
A) 0.0916
B) 0.1832
C) 0.0458
D) 0.0183

Accepted Answer

The probability of getting exactly 5 tails in 15 tosses of a fair coin can be calculated using the binomial probability formula: P(X = k) = (n choose k) * p^k * (1-p)^(n-k), where n is the number of trials (15), k is the number of successes (5), and p is the probability of success on a single trial (0.5 for a fair coin). Plugging in the values, we get P(5 tails) = (15 choose 5) * (0.5)^5 * (0.5)^(15-5) = 0.0916.

Question 14

Find the probability.
-A child rolls a 6-sided die 6 times. What is the probability of the child rolling no more than three Twos? Round to the nearest ten-thousandth.
A) 0.3812
B) 0.6774
C) 0.9913
D) 0.9649

Accepted Answer

The probability of rolling no more than three Twos in six rolls of a 6-sided die can be calculated using the binomial probability formula. The probability of rolling a Two (success) is $ \frac{1}{6} $ and not rolling a Two (failure) is $ \frac{5}{6} $. We calculate the probability for 0, 1, 2, and 3 successes (rolling a Two) and sum these probabilities. The calculations for each of these scenarios involve combinations and the probabilities of successes and failures raised to the appropriate powers. The sum of these probabilities gives the total probability of rolling no more than three Twos, which is approximately 0.9913, making option C the correct answer.

Question 15

Find the probability. Round to the nearest ten-thousandth when necessary.
-A family has five children. The probability of having a girl is 1/2. What is the probability of having At least 3 boys?
A) 0.5
B) 0.4688
C) 0.3125
D) 0.1563

Accepted Answer

The answer of Find the probability. Round to the nearest...

Question 16

Find the probability. Round to the nearest ten-thousandth when necessary.
-A family has five children. The probability of having a girl is 1/2. What is the probability of having At least 4 girls?
A) 0.1563
B) 0.0313
C) 0.3125
D) 0.1875

Accepted Answer

The probability of having at least 4 girls means having either 4 girls or 5 girls. Using the binomial probability formula, P(X=k) = C(n, k) * (p^k) * ((1-p)^(n-k)), where n=5, p=1/2, and k is the number of girls. Calculate for k=4 and k=5, then sum the probabilities: P(4 girls) = C(5, 4) * (1/2)^4 * (1/2)^1 = 5 * 1/32 = 5/32, P(5 girls) = C(5, 5) * (1/2)^5 = 1/32. Total probability = 5/32 + 1/32 = 6/32 = 0.1875.

Question 17

Find the probability. Round to the nearest ten-thousandth when necessary.
-A family has five children. The probability of having a girl is 1/2. What is the probability of having No more than 3 boys?
A) 0.5
B) 0.8125
C) 0.3125
D) 0.9688

Accepted Answer

The answer of Find the probability. Round to the nearest...

Question 18

Find the probability.
-A die is rolled 20 times and the number of twos that come up is tallied. Find the probability of Getting exactly four twos. Round to the nearest thousandth when necessary.
A) 0.083
B) 0.101
C) 0.075
D) 0.202

Accepted Answer

The answer of Find the probability.
-A die is rolled 20 times and...

Question 19

Find the probability.
-What is the probability that 20 rolls of a fair die will show 8 threes? Round to the nearest Ten-thousandth.
A) 0.0168
B) 0.0017
C) 0.0084
D) 0.0042

Accepted Answer

The answer of Find the probability.
-What is the probability that 20 rolls...

Question 20

Find the probability. Round to the nearest ten-thousandth when necessary.
-A coin is biased to show 44% heads and 56% tails. The coin is tossed twice. What is the probability That the coin turns up tails on both tosses?
A) 0.12
B) 0.56
C) 0.44
D) 0.3136

Accepted Answer

The probability of getting tails on both tosses is found by multiplying the probability of getting tails on one toss by itself (since the coin is tossed twice and the events are independent). Thus, $0.56 \times 0.56 = 0.3136$.

Quiz 11: Probability

Find the probability. Round to the nearest ten-thousandth when necessary. -A fair coin is tossed 5 times. What is the probability of no heads?

Find the probability. Round to the nearest ten-thousandth when necessary. -A coin is biased to show 43% heads and 57% tails. The coin is tossed twice. What is the probability That the coin turns up heads on the second toss?

Find the probability. Round to the nearest ten-thousandth when necessary. -A fair coin is tossed 5 times. What is the probability of exactly 3 head(s) ?

Find the probability. -What is the probability that 8 rolls of a fair die will show three threes? Round to the nearest Ten-thousandth.

Find the probability. -A child rolls a 6-sided die 6 times. What is the probability of the child rolling exactly two fours? Round to the nearest ten-thousandth.

Find the probability. -A die is rolled 20 times and the number of twos that come up is tallied. Find the probability of Getting more than three twos. Round to the nearest thousandth when necessary.

Find the probability. -A child rolls a 6-sided die 6 times. What is the probability of the child rolling exactly four fives? Round to the nearest ten-thousandth.

Find the probability. Round to the nearest ten-thousandth when necessary. -A coin is biased to show 45% heads and 55% tails. The coin is tossed twice. What is the probability That the coin turns up heads once and tails once?

Find the probability. -A die is rolled 20 times and the number of twos that come up is tallied. Find the probability of Getting exactly five twos. Round to the nearest thousandth when necessary.

Find the probability. -A child rolls a 6-sided die 6 times. What is the probability of the child rolling exactly three sixes? Round to the nearest ten-thousandth.

Find the probability. -A die is rolled 20 times and the number of twos that come up is tallied. Find the probability of Getting exactly two twos. Round to the nearest thousandth when necessary.

Find the probability. -In a certain college, 33% of the physics majors are ethnic minorities. A random sample of 10 Physics majors is chosen. Find the probability that exactly 2 are ethnic minorities. Round to the Nearest ten-thousandth.

Find the probability. Round to the nearest ten-thousandth when necessary. -What is the probability that 15 tosses of a fair coin will show 5 tails?

Find the probability. -A child rolls a 6-sided die 6 times. What is the probability of the child rolling no more than three Twos? Round to the nearest ten-thousandth.

Find the probability. Round to the nearest ten-thousandth when necessary. -A family has five children. The probability of having a girl is 1/2. What is the probability of having At least 3 boys?

Find the probability. Round to the nearest ten-thousandth when necessary. -A family has five children. The probability of having a girl is 1/2. What is the probability of having At least 4 girls?

Find the probability. Round to the nearest ten-thousandth when necessary. -A family has five children. The probability of having a girl is 1/2. What is the probability of having No more than 3 boys?

Find the probability. -A die is rolled 20 times and the number of twos that come up is tallied. Find the probability of Getting exactly four twos. Round to the nearest thousandth when necessary.

Find the probability. -What is the probability that 20 rolls of a fair die will show 8 threes? Round to the nearest Ten-thousandth.

Find the probability. Round to the nearest ten-thousandth when necessary. -A coin is biased to show 44% heads and 56% tails. The coin is tossed twice. What is the probability That the coin turns up tails on both tosses?