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

a) one student is chosen from classroom a, then a student is chosen from classroom b.  

step-by-step explanation:

independent events are ones in which the probability of one event does not affect the probability of the second event.

one student is chosen from classroom a; this does not affect the chances of choosing a student from classroom b.   this makes these independent events.

when one card is chosen from a standard deck and then set aside before a second card is chosen, the probability of the second card being chosen changes.   this makes them dependent events.

when one student is chosen from classroom a and then a second student is chosen from classroom a, the probability of choosing the second student changes.   this makes them dependent events.

when a letter is chosen from the alphabet and then a second letter is chosen, the probability of choosing the second letter changes.   this makes them dependent events.