COT 3100 Homework 10

Assume that the probability a child is a boy is 0.51 and that the sexes of children born into a family are independent. Choose the expression that gives the probability that a family of five children has exactly three boys.

(53) (0.51)^3 (1−0.51)^5−3

Assume that the probability a child is a boy is 0.51 and that the sexes of children born into a family are independent. Choose the expression that gives the probability that a family of five children has at least one boy.

1 - 0.49^5

What is the probability that Bo, Colleen, Jeff, and Rohini win the first, second, third, and fourth prizes, respectively, in a drawing if 50 people enter a contest and satisfying the following conditions? (Enter the value of probability in decimals. Round the answer to two decimal places.) No one can win more than one prize.

1.81 × 10^-7

Consider the set of all permutations of {1, 2, . . ., n} where n ≥ 4. What is the probability of selecting a permutation in which 1 precedes 2?

1/2

Consider the set of all permutations of {1, 2, . . ., n} where n ≥ 4. What is the probability of selecting a permutation in which 2 precedes 1?

1/2

What is the probability that the sum of the numbers on two dice is even when they are rolled? (Enter the value of probability in decimal format.)

1/2 0.5

Consider the set of all permutations of {1, 2, . . ., n} where n ≥ 4. What is the probability of selecting a permutation in which n precedes 1 and 2?

1/3

Consider the set of all permutations of {1, 2, . . ., n} where n ≥ 4. What is the probability of selecting a permutation in which n precedes 1 and n − 1 precedes 2?

1/4

What is the probability that a fair die comes up six when it is rolled? (Enter the value of probability in decimals. Round the answer to two decimal places.)

1/6 0.17

Assume that the year has 366 days and all birthdays are equally likely. Find the probability that two people chosen at random were born on the same day of the week.

1/7

Consider the set of all permutations of {1, 2, . . ., n} where n ≥ 4. What is the probability of selecting a permutation in which 1 immediately precedes 2?

1/n

Find the probability of each outcome when a loaded die is rolled, if a 3 is twice as likely to appear as each of the other five numbers on the die.

p(3)= 2/7 and p(x)=1/7 for x = 1, 2, 4, 5, 6.

Find the probability of winning a lottery by selecting the correct six integers, where the order in which these integers are selected does not matter, from the positive integers not exceeding the given integers. (Enter the value of probability in decimals. Round the answer to one decimal place.) The probability of winning a lottery by selecting the correct six integers from the positive integers not exceeding 52 is _____ × 10-8.

4.9

What is the probability that a card selected at random from a standard deck of 52 cards is an ace or a heart? (Enter the value of probability in decimals. Round the answer to two decimal places.)

4/13 0.31

Find the probability of winning a lottery by selecting the correct six integers, where the order in which these integers are selected does not matter, from the positive integers not exceeding the given integers. (Enter the value of probability in decimals. Round the answer to one decimal place.) The probability of winning a lottery by selecting the correct six integers from the positive integers not exceeding 50 is _____ × 10^-8.

6.3

A pair of dice is loaded. The probability that a 4 appears on the first die is 2/7, and the probability that a 3 appears on the second die is 2/7. Other outcomes for each die appear with probability 1/7. Identify the correct procedure to find the probability of 7 appearing as the sum of the numbers when the two dice are rolled.

The two dice are independent. The probabilities of each outcome on each die are p((1, 6)) = 1/7⋅1/7=1/49, p((2, 5)) = 1/7⋅1/7=1/49, p((3, 4)) = 1/7⋅1/7=1/49, p((4, 3)) = 2/7⋅2/7=4/49, p((5, 2)) = 1/7⋅1/7=1/49, and p((6, 1)) = 1/7⋅1/7=1/49. Hence, the probability of rolling a 7 is 9/49.