Question

A candy machine has 9 buttons of which one never works, two work one-half the time, and the rest work all the time. A coin is inserted and a button is pushed at random.

a) What is the probability that no candy is received?

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

c) If candy is received, what is the probability that one of the buttons that work one-half the time was the one pushed?

Answer 1

Given data

Total number of button(n)=9

Number of button never work (A) =1

Probability of pushing that button P(A)=1/9=0.12

Number of button work half the time (B) =2

Probability of pressing that button P(A)=2/9=0.23

Number of button always (C) =6

Probability of pressing that button P(C)=6/9=0.67

a) As we can see from the given data above

The Probability that one not get the candy when he will press the A key is 100% and when he will press the key B then the chances are 50% because half the time it found not working

So probability of getting no candy =P(A)+1/2 P(B)=0.12+1/2. *0.23=0.235

b) Now it is given that he gets no candy .so it is that he pressed either One who never gives candy and two other who half of the time gives the candy

So number of button which may not give candy=3

No of buttom never gives candy=1

Probablity of getting that button =1/3=0.34

c) now given that candi is received

So number of button that can give candy =8

Number of button which works half of the time =2

So Probablity of pressing that buttons =2/8=0.25