Tom is making calls door to door in a neighborhood of 45 houses to give out gift cards for a new supermarket. He leaves a gift card only on those calls for which the door is answered. On any call the probability of the door being answered is 40%. a) Find the probability that Tom gives away at most 2 gift cards in the first 5 calls. b) Given that he has given away exactly 2 gift cards on his first 5 calls, find the probability that Tom will give away the 5th gift card on the 10th call. c) Find the expected total number of cards given out when he is done.

A) 0,7

B) 0,14

C) 18

Step-by-step explanation:

40% is 2/5, so the propbability to answer is 2/5 and to not answer is 3/5.

a) at most 2 cards mean it can be 0 card, 1card and 2cards.

For 0, brobability is (3/5) ^5=0,08

For 1, probability is 5 * (2/5) (3/5) ^4=0,26

(5 is number of combination when door is answered, on first call, 2nd, 3th, 4th or 5th)

For 2, probability is (5/choose 2) (2/5) ^2 (3/5) ^3=10 (27/3125) = 0,36

So 0,08+0,26+0,36=0,7

B) now we have 5 new more calls and he had to give 3 cards and 3th is on 5th call.

6 * (3/5) ^2 (2/5) ^3=0,14

C) the probability is 40% so expected number is 45*0,4=18.