Question

A candy machine has 10 buttons of which one never works, two workone-half the time, and the rest work all the time. A coin isinserted and a button is pushed at random.

b. If no candy is received, what is the probability that the buttonthat never works was the one pushed?

Answer 1

0.5 probability of pressing the button that doesn't work GIVEN that no candy is received.

Explanation:

1) The probability of pushing the button that never works: 1/10 = 0.1

2) The probability of pushing one of the buttons that work half the time:

2/10 = 0.2

The probability of (2) not working = 0.5

Overall probability of (2) pressed and not working = 0.5 * 0.2 = 0.1

Probability of non working button being pushed GIVEN no candy is received will be: 0.1 / (0.1+0.1) = 0.1/0.2 = 0.5