Suppose that we investigate an apple store shop and saw on average that out of 20 customer, 16 of them want to buy the newest iPhone. We select 50 customer randomly, find the probability that (5 point each):

1. more than 37 customers want to buy the newest iPhone.
2. Exactly 40 customers want to buy the newest iPhone.
3. What is the variance on the number of purchased iPhone.
4. Name the distribution.

Suppose that we saw thunderstorm on average rate of 5 per month during Fall. Calculate the following(5 point each):

1. The probability that during 2 month we see at most 6 thunderstorm.
2. The probability that during 3 months we see exactly 10 thunderstorms.
3. What is the expected value on the number of the thunderstorms?
4. Name the distribution.

We have a four sided die and the die is not fair meaning that the probability of getting "1" is 3 times (*3) the probability of getting other values (2,3,4) but the probability of the other possibilities are equal. We define the random variable Z which shows the number when we roll the die. Calculate the following(5 point each):

1. What is the expected value of Z?
2. What is the probability mass function for the random variable Z?
3. Is it Uniform distribution? Explain your answer.

We have a bag containing 5 red marbles and 8 blue marbles. we draw 7 marbles randomly without replacement. Calculate the following(5 point each):

1. The probability that we draw 3 blue and 4 red marbles.
2. The probability that we draw at most 6 blue marbles.
3. Name the distribution.