Question 1

Determine the sample space for the experiment. ​
Two prize winners are selected from six people: A,B,C,D,E,and F.
​
A)S = {AB,AC,AD,AE,BC,BD,BE,CD,CE,DE}
B)S = {AB,AC,AD,AE,AF}
C)S = {AB,AC,AD,AE,AF,BC,BD,BE,BF,CD,CE,CF,DE,DF,EF}
D)S = {AB,AC,AD,BC,BD,CD}
E)S = {AB,CD,EF}

Accepted Answer

The sample space should include all possible combinations of two people selected from the group of six. Option C has all 15 possible combinations listed, making it the best choice. The other options either have missing combinations or include combinations that are not possible with only two prize winners.

Question 2

You are given the probability that an event will not happen.Find the probability that the event will happen. $P ( E ) = \frac { 4 } { 15 }$
A) $\frac { 4 } { 15 }$
B)0
C)1
D) $\frac { 11 } { 15 }$
E) $\frac { 11 } { 30 }$

Accepted Answer

The probability that an event will happen is 1 minus the probability that it will not happen. Given $P(E) = \frac{4}{15}$, the probability that the event will happen is $1 - \frac{4}{15} = \frac{11}{15}$.

Question 3

Find the probability for the experiment of drawing two marbles (without replacement)from a bag containing 2 green,6 yellow and 3 red marbles such that both marbles are yellow.
A)​ $\frac { 1 } { 3 }$
B)​ $\frac { 6 } { 5 }$
C)​ $\frac { 36 } { 121 }$
D)​ $\frac { 18 } { 55 }$
E)​ $\frac { 3 } { 11 }$

Accepted Answer

The answer of Find the probability for the experiment of...

Question 4

Determine the sample space for the experiment.
Three prize winners are selected from six people: A,B,C,D,E,and F.

Accepted Answer

The answer of Determine the sample space for the experiment.
Three...

Question 5

In a sample of 20 hand-held calculators,15 are known to be nonfunctional.If 7 of these calculators are selected at random,what is the probability that exactly 5 in the selection are nonfunctional? Round to the nearest thousandth.
A)0
B)0.714
C)0.387
D)0.467
E)0.750

Accepted Answer

We can use the binomial probability formula to solve this problem:
P(X=5) = (15 choose 5) * (5 choose 2) / (20 choose 7) = 3003 * 10 / 77520 = 0.387 (rounded to the nearest thousandth)

Question 6

You are given the probability that an event will happen.Find the probability that the event will not happen. $P ( E ) = 0.87$
A)0.87
B)0.13
C)0.065
D)0
E)1

Accepted Answer

The probability of an event not happening is equal to 1 minus the probability of the event happening. Therefore, the answer is 1 - probability of the event happening. In this case, since only the probability of the event happening is given, we subtract it from 1 to get the probability of the event not happening. Therefore, the answer is 0.13, which is option B. Option A (0.87) is the incorrect answer as it is the probability of the event happening. Option C (0.065) is not a valid answer as it is too low and cannot be the probability of something occurring or not occurring. Option D (0) cannot be the answer since the probability of something not happening cannot be 0. Finally, option E (1) is also incorrect as there is no event with a 100% chance of happening, and the question does not provide enough information to conclude that the event will certainly not happen.

Question 7

Find the probability for the experiment of drawing two marbles (without replacement)from a bag containing three green,five yellow,and two red marbles such that the marbles are different colors.
A) $\frac { 31 } { 90 }$
B) $\frac { 31 } { 15 }$
C) $\frac { 31 } { 45 }$
D) $\frac { 1 } { 5 }$
E)0

Accepted Answer

The answer of Find the probability for the experiment of...

Quiz 58: Probability

Determine the sample space for the experiment. Two prize winners are selected from six people: A,B,C,D,E,and F.

You are given the probability that an event will not happen.Find the probability that the event will happen. $P ( E ) = \frac { 4 } { 15 }$

Find the probability for the experiment of drawing two marbles (without replacement) from a bag containing 2 green,6 yellow and 3 red marbles such that both marbles are yellow.

Determine the sample space for the experiment. Three prize winners are selected from six people: A,B,C,D,E,and F.

In a sample of 20 hand-held calculators,15 are known to be nonfunctional.If 7 of these calculators are selected at random,what is the probability that exactly 5 in the selection are nonfunctional? Round to the nearest thousandth.

You are given the probability that an event will happen.Find the probability that the event will not happen. $P ( E ) = 0.87$

Find the probability for the experiment of drawing two marbles (without replacement) from a bag containing three green,five yellow,and two red marbles such that the marbles are different colors.