I play a gambling game in which I will win k-2 dollars with probability for any

Question

I play a gambling game in which I will win k-2 dollars with probability for any natural number k. In other words, 2k I will lose $1 with probability 1/2 I will lose $O and win $0 with probability 1/4 I will win $1 with probability 1/8 I will win $2 with probability 1/16 I will win $3 with probability 1/32 a. What is the probability that I win at least $1 and less than $4? b. What is the probability that I win more than $2? 7. Among 18 students in a room, 7 study mathematics, 10 study science, and 10 study computer programming. Also, 3 study mathematics and science, 4 study mathematics and computer programming, and 5 study science and computer programming. We know that 1 student studies al three subjects. How many of these students study none of the three subjects?

Explanation / Answer

a) probability of winning at least $1 and less than $4 =P(X=1)+P(X=2)+P(X=3) =(1/8)+(1/16)+(1/32) =7/32

b) probability that I win more than $2 =1-P(win at most $2)

=1-(P(X=-1)+P(X=0)+P(X=1)+P(X=2)) =1-(1/2+1/4+1/8+1/16) =1-15/16 =1/16

c)

here let studying math is A ; science B and computer programming =C

hence

therefore number of students study at least one f them =

hence number of students study none of three =18-16 =2

N(T)= 18 N(A)= 7 N(B)= 10 N(C)= 10 N(AnB)= 3 N(BnC)= 5 N(AnC)= 4

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