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?

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

Step-by-step 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