Question

A) Triomino's Pizza sells only pizza. They offer five types of crust, two types of cheese, three meat toppings and nine vegetable toppings. If you must order exactly one type of cheese, one meat topping and one vegetable topping on your pizza, how many different pizzas can you order at Triomino's Pizza?

B) A boy owns 1 pairs of pants, 8 shirts, 8 ties, and 5 jackets. How many different outfits can he wear to school if he must wear one of each item?

He can wear  different outfits.

C) Malik owns all four books in the Wrinkle in Time series. In how many different orders can he place all of them on the top shelf of his bookshelf?

D)

As shown above, a classic deck of cards is made up of 52 cards. Suppose one card is selected at random and calculate the following probabilities.

Round solutions to three decimal places, if necessary.

The probability that a 7 of Hearts is selected is .

The probability that a Spade or Diamond is selected is .

The probability that a number smaller than 3 (counting the ace as a 1) is selected is .

E)

The probability that a randomly selected IRSC student is an athlete is 0.18. The probability that a randomly selected IRSC student is a biology major is 0.16. The probability that a randomly selected IRSC student is a biology major and an athlete is 0.13.

Calculate the following probabilities. Round solutions to three decimal places, if necessary.

Determine the probability that a randomly selected IRSC student is a biology major, given the student is an athlete.

P(P(biology major | athlete)=)=

Determine the probability that a randomly selected IRSC student is an athlete, given the student is a biology major.

P(P(athlete | biology major)

Answer 1

A)

The number of different pizzas you can order at Triomino's Pizza = 5*2*3*9 = 270

B)

Number of different outfits that the boy can wear = 2*8*8*5 = 640

C)

Number of different orders possible = 4! = 24

D)

The probability that a 7 of Hearts is selected is 1/52

The probability that a spade or Diamond is selected is 26/52 = 1/2

The probability that a number smaller than 3 is selected = (2*4)/52 = 2/13

E)

P(Biology major) = 0.16,

P(athlete) = 0.18,

P(Biology major and athlete) = 0.13

Probability that a randomly selected IRSC student is a biology major, given the student is an athlete = P(Biology major | athlete)

= P(Biology major and athlete)/P(athlete)

= 0.13/0.18 = 0.722

P(athlete | biology major) = P(athlete and Biology major)/P(biology major)

= 0.13/0.16 = 0.8125