Answer:
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.