Question

You come home from Brian’s Orchard with a big brown bag of apples: 23 Granny Smiths, 14 Honey Crisp and 31 Red Delicious. What is the probability you reach in and pull out: a. one of each? b. 4 Honey Crisps c. 2 G. Smiths & 1 R. Delicious

Answer 1

A.) 4991/157216

B.) 2401/1336336

C.) 16399/314432

Explanation:

Given the following :

Granny Smith = 23

Honey crisp = 14

Red delicious = 31

Probability = (number of required outcome / number of possible outcomes)

Number of possible outcomes = 23 + 14 + 31 = 68

With replacement :

A.) one of each :

P(granny Smith) × P(Honey crisp) × P(Red delicious)

P(granny Smith) = 23/68

P(Honey crisp) = 14/68 = 7/34

P(red delicious) = 31/68

(23/68 × 7/34 × 31/68) = 4991/157216

B) 4 honey crisp:

P(4 Honey crisp) = P(honey crisp) × P(honey crisp) × P(honey crisp) × P(honey crisp)

7/34 × 7/34 × 7/34 × 7/34 = 2401/1336336

C.) 2 granny Smith and 1 red delicious

P(granny Smith) × P(granny Smith) × P(red delicious)

23/68 × 23/68 × 31/68 = 16399/314432