Question

A contestant on a game show must choose 2 of 16 boxes. Once a box is chosen, it is removed from the game. Of the 16 boxes, 3 contain money, 5 contain traveling prizes, and 8 are empty. What is the probability that both boxes are empty?

Answer 1

Answer:

7 / 30

Step-by-step explanation:

This is a selection without replacement probability :

Total boxes = 16

With money = 3

With traveling prices = 5

Empty = 8

P(choosing 2 empty boxes) :

P(empty) * P(empty)

P(empty) = Number of empty boxes / total number of boxes

First pick = empty

P(empty) = 8 / 16 = 1/2

Without replacement :

Second pick = empty

P(empty) = 7 / 15

P(choosing 2 empty boxes) = 1/2 * 7/15 = 7 /30