Question 1

Find the indicated probability. Round your answer to 6 decimal places when necessary.
-Find the probability of tossing 5 tails, then 5 heads, on the first 10 tosses of a fair coin.

Accepted Answer

The probability of tossing a tail with a fair coin is 1/2, and the same goes for tossing a head. Since each toss is independent, the probability of tossing 5 tails followed by 5 heads in 10 tosses is (1/2)^10 = 1/1024 = 0.000977.

Question 2

Solve the problem.
-How many 3-digit numbers can be formed using the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, if repetition of digits is allowed?

Accepted Answer

For a 3-digit number, the first digit can be any of the 9 options (1-9, since it can't be 0), and the second and third digits can be any of the 10 digits (0-9), allowing repetition. Thus, the total number of combinations is 9 * 10 * 10 = 900. However, the question asks for the number of 3-digit numbers that can be formed, which includes all numbers from 100 to 999. Since 999 is the last 3-digit number, subtracting 100 (the first 3-digit number) from 999 gives 899, but since both 100 and 999 are inclusive, we add 1 back, resulting in 900 total numbers, which is not listed as an option. The correct interpretation should be calculating the total possibilities directly, which is indeed 900, not 1000. My explanation mistakenly suggested adding an extra step, but the correct calculation directly yields 900 possibilities for forming 3-digit numbers with the given conditions.

Question 3

Solve the problem.
-Suppose you are playing a game of chance. If you bet $7 on a certain event, you will collect $252 (including your $7 bet)if you win. Find the odds used for determining the payoff.

Accepted Answer

The payoff is $252, including the original $7 bet, meaning the profit is $245 ($252 - $7). The odds are calculated based on the profit, not the total payout. Therefore, for every $7 bet, you win $245, which simplifies to a ratio of 35:1.

Question 4

Find the indicated probability. Round your answer to 6 decimal places when necessary.
-Two 6-sided dice are rolled. What is the probability that the two numbers obtained differ by more than 2?

Accepted Answer

The answer of Find the indicated probability. Round your answer...

Question 5

Solve the problem.
-A poker hand consists of 5 cards dealt from an ordinary deck of 52 playing cards. How many different hands are there consisting of four hearts and one spade?

Accepted Answer

The answer of Solve the problem.
-A poker hand consists of...

Question 6

Find the indicated probability. Round your answer to 6 decimal places when necessary.
-Find the probability of rolling 3 successive 2s with 3 rolls of a fair die.

Accepted Answer

The probability of rolling a 2 on a fair die is 1/6. For three successive rolls, the probability is (1/6) * (1/6) * (1/6) = 1/216, which is approximately 0.004630.

Question 7

Solve the problem.
-The table shows the prizes and probabilities of winning (on a single $1 ticket)for a particular state lottery. Find the expected value of the winnings for a single lottery ticket. $\begin{array}{c|l}
\text { Prize (dollars) } & \text { Probability } \
\hline 5 \text { million (jackpot) } & 1 \text { in } 76,275,360 \
150,000 & 1 \text { in } 2,179,296 \
5000 & 1 \text { in } 339,002 \
150 & 1 \text { in } 9686 \
100 & 1 \text { in } 7705 \
5 & 1 \text { in } 220 \
2 & 1 \text { in } 102 \
1 & 1 \text { in } 62
\end{array}$

Accepted Answer

The answer of Solve the problem.
-The table shows the prizes...

Question 8

Solve the problem.
-The odds on (against)your bet are 4 to 1. If you bet $26 and win, how much will you gain? Use the definition of odds in betting.

Accepted Answer

Odds of 4 to 1 against a bet mean for every $1 bet, you win $4 if successful. So, for a $26 bet, the gain is 4 * $26 = $104.

Question 9

Solve the problem.
-A restaurant offers pizzas with 3 types of crust, 7 different toppings, and in 6 different sizes. How many different pizzas could be ordered?

Accepted Answer

The number of different pizzas that can be ordered is found by multiplying the number of options for each category together: 3 types of crust * 7 different toppings * 6 different sizes = 126 different pizzas.

Question 10

Decide whether events A and B are overlapping or non-overlapping.
-A card is drawn at random from a deck of cards. Event A is that the card obtained is a face card and event B is that the card obtained is a spade.

Accepted Answer

Events A and B are overlapping because there are face cards (Jack, Queen, King) that are also spades, meaning a card can simultaneously be a face card and a spade.

Question 11

Find the indicated probability. Round your answer to 6 decimal places when necessary.
-In January in a certain city the unconditional probability of rain on any given day of the month is 0.400. But the probability of rain on a day that follows a rainy day is 0.600 and the probability of
Rain on a day following a nonrainy day is 0.250. Find the probability of rain on three randomly
Selected consecutive days in January.

Accepted Answer

The probability of rain on three consecutive days involves the initial probability of rain on the first day and the conditional probabilities for the subsequent days. The calculation is 0.400 (probability of rain on the first day) * 0.600 (probability of rain on the second day, given the first day was rainy) * 0.600 (probability of rain on the third day, given the second day was rainy) = 0.144.

Question 12

Solve the problem.
-A signal is made by placing 3 flags, one above the other, on a flag pole. If there are 6 different flags available, how many possible signals can be flown?

Accepted Answer

Since there are 6 choices for the first flag, 5 remaining choices for the second flag, and 4 remaining choices for the third flag, the total number of possible signals is 6 * 5 * 4 = 120.

Question 13

Find the indicated probability. Round your answer to 6 decimal places when necessary.
-A card is drawn at random from a well-shuffled deck of 52 cards. What is the probability of drawing a face card or a 5?

Accepted Answer

In a deck of 52 cards, there are 12 face cards (Jacks, Queens, Kings of each suit) and 4 fives (one from each suit). However, since the question asks for the probability of drawing a face card or a 5, and these events are mutually exclusive (a card cannot be both a face card and a 5), we simply add the probabilities of each event. Thus, the probability is $\frac{12 + 4}{52} = \frac{16}{52} = \frac{4}{13}$.

Question 14

Solve the problem.
-A pollster wants to minimize the effect the order of the questions has on a person's response to a survey. How many different surveys are required to cover all possible arrangements if there are 6
Questions on the survey?

Accepted Answer

The number of different surveys required to cover all possible arrangements of 6 questions is calculated by finding the factorial of 6, which is 6! = 6 × 5 × 4 × 3 × 2 × 1 = 720.

Question 15

Find the indicated probability. Round your answer to 6 decimal places when necessary.
-If three fair coins are tossed, what is the probability of not tossing three heads?

Accepted Answer

The total number of outcomes when tossing three coins is $2^3 = 8$. The only outcome not included is getting three heads, which is 1 out of the 8 possible outcomes. Therefore, the probability of not tossing three heads is $1 - \frac{1}{8} = \frac{7}{8}$.

Question 16

Solve the problem. Round your answer to 2 decimal places when necessary.
-In a given year, the population of a certain country is about 224 million. The overall birth rate is 18.2 births per 1000. The overall death rate is 10.1 deaths per 1000. Based on births and deaths
Alone (not counting immigration), about how much does the population of the country increase
During this year?

Accepted Answer

To calculate the population increase based on births and deaths alone, we first find the number of births and deaths per 1000 people, then apply these rates to the entire population. The birth rate is 18.2 births per 1000, leading to 224 million * (18.2/1000) = 4.0768 million births. The death rate is 10.1 deaths per 1000, leading to 224 million * (10.1/1000) = 2.2624 million deaths. The net increase is the births minus the deaths: 4.0768 million - 2.2624 million = 1.8144 million, which rounds to 1.81 million.

Question 17

Make a probability distribution for the given set of events.
-When four fair coins are tossed, sixteen equally likely outcomes are possible as shown below: H?H? H?HT HHTH HHTT
HTHH HTHT HTTH HTTT
THHH THHT THTH THTT
TTHH TTHT TTTH TTTT Make a probability distribution for the number of tails when four fair coins are tossed.

Accepted Answer

The correct probability distribution for the number of tails when four fair coins are tossed is: 0 Tails: 1/16, 1 Tail: 1/4, 2 Tails: 3/8, 3 Tails: 1/4, 4 Tails: 1/16.

Question 18

Solve the problem.
-A musician plans to perform 5 selections for a concert. If he can choose from 9 different selections, how many ways can he arrange his program?

Accepted Answer

The number of ways to arrange 5 selections out of 9 is calculated using permutations since the order of the selections matters. This is given by 9P5 = 9! / (9-5)! = 9*8*7*6*5 = 15,120.

Question 19

Solve the problem. Round your answer to 2 decimal places when necessary.
-A U.S. city with a population of 2.3 million reports 14,993 deaths. What is the death rate in deaths per 1000 people?

Accepted Answer

To find the death rate per 1000 people, divide the number of deaths by the population and then multiply by 1000: (14,993 / 2,300,000) * 1000 = 6.52 deaths per 1000 people.

Question 20

Solve the problem.
-If 6 newborn babies are randomly selected, how many different gender sequences are possible?

Accepted Answer

For each baby, there are 2 possible genders (male or female), and since there are 6 babies, the number of different gender sequences is $2^6 = 64$.

Quiz 7: Probability: Living With the Odds

Find the indicated probability. Round your answer to 6 decimal places when necessary. -Find the probability of tossing 5 tails, then 5 heads, on the first 10 tosses of a fair coin.

Solve the problem. -How many 3-digit numbers can be formed using the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, if repetition of digits is allowed?

Solve the problem. -Suppose you are playing a game of chance. If you bet $7 on a certain event, you will collect $252 (including your $7 bet) if you win. Find the odds used for determining the payoff.

Find the indicated probability. Round your answer to 6 decimal places when necessary. -Two 6-sided dice are rolled. What is the probability that the two numbers obtained differ by more than 2?

Solve the problem. -A poker hand consists of 5 cards dealt from an ordinary deck of 52 playing cards. How many different hands are there consisting of four hearts and one spade?

Find the indicated probability. Round your answer to 6 decimal places when necessary. -Find the probability of rolling 3 successive 2s with 3 rolls of a fair die.

Solve the problem. -The odds on (against) your bet are 4 to 1. If you bet $26 and win, how much will you gain? Use the definition of odds in betting.

Solve the problem. -A restaurant offers pizzas with 3 types of crust, 7 different toppings, and in 6 different sizes. How many different pizzas could be ordered?

Decide whether events A and B are overlapping or non-overlapping. -A card is drawn at random from a deck of cards. Event A is that the card obtained is a face card and event B is that the card obtained is a spade.

Solve the problem. -A signal is made by placing 3 flags, one above the other, on a flag pole. If there are 6 different flags available, how many possible signals can be flown?

Find the indicated probability. Round your answer to 6 decimal places when necessary. -A card is drawn at random from a well-shuffled deck of 52 cards. What is the probability of drawing a face card or a 5?

Solve the problem. -A pollster wants to minimize the effect the order of the questions has on a person's response to a survey. How many different surveys are required to cover all possible arrangements if there are 6 Questions on the survey?

Find the indicated probability. Round your answer to 6 decimal places when necessary. -If three fair coins are tossed, what is the probability of not tossing three heads?

Solve the problem. -A musician plans to perform 5 selections for a concert. If he can choose from 9 different selections, how many ways can he arrange his program?

Solve the problem. Round your answer to 2 decimal places when necessary. -A U.S. city with a population of 2.3 million reports 14,993 deaths. What is the death rate in deaths per 1000 people?

Solve the problem. -If 6 newborn babies are randomly selected, how many different gender sequences are possible?