Question

1. I am going to roll a dice. What is complement of rolling a 1?

2. If you roll five dice, what is the probability that they will all turn up the same?

3. A Ph.D. graduate has applied for a job with two colleges: A and B. The graduate feels that she has a 60% chance of receiving an offer from college A. She also feels that she has a 50% chance of receiving an offer from college B. If she receives an offer from college B, she believes that she has an 80% chance of also receiving an offer from college A.

a. If she receives an offer from college B, what is the probability that she will not receive an offer from college A?

b. What is the probability that both colleges A and B will make her an offer?

c. What is the probability that at least one college will make her an offer?

Answer 1

Solution:-)

a) If we roll a die then sample space wil,be S= {1,2,3,4,5,6}.

The probability of not occuring 1 on upper face will be 5/6 , if 1 did not occur then {2,3,4,5,6} have occured.

b) There are five dice and probability of occuring a number si 1/6 and now when second dice is rolled then the probability of occuring that number is 1/6 and so on for the probability of occuring the same number on 5 dice is 1/6.

The required probability is

3) Probability of receiving an offer from college A.

Probability of receiving an offer from college B.

Probability that if she receives an offer from college B, then the probability is 80% of receiving an offer from college A.

a)

b)

c)