An urn contains 5 white and 10 black balls. A fair die is rolled and that number of balls is randomly chosen from the urn. What is the probability that all of the balls selected are white? What is the conditional probability that the die landed on 3 if all the balls selected are white?

Part A:

The probability that all of the balls selected are white:

Part B:

The conditional probability that the die landed on 3 if all the balls selected are white:

Step-by-step explanation:

A is the event all balls are white.

D_i is the dice outcome.

Sine the die is fair:

for i∈{1,2,3,4,5,6}

In case of 10 black and 5 white balls:

Part A:

The probability that all of the balls selected are white:

Part B:

The conditional probability that the die landed on 3 if all the balls selected are white:

We have to find

The data required is calculated above:

answer: all of the odd numbers were opened

the first person was the one that was opening all of the lockers. since one is odd, this causes all of the odd number lockers to be opened in the end.