bobby continues shooting 3 moving targets until he knocks all of the down.

Question

A) find the probability that Bobby will require exactly 5 shots to accomplish his goal

B) find the expected number of shots it takes to knock all the targets down

Answer 1

A)

Let p = probability of hitting a target on any one try, Let p=1/2

then P(3 in 5 tries) = 5C3(1/2)^3(1/2)^2

= 5!/3!2!)(1/2)^5 = 10/2^5

= 10/32

in general P(3 in 5 tries) = 10(p)^3(q)^2 where q =1-p

=10p^3(1-p)^2 = 10p^3(1-2p+p^2)

= 10(p^3-2p^4 +p^5)

if p=1/2

= 10((1/2)^3 -2(1/2)^4 + (1/2)^5

=10(1/8 -1/8+1/32)

= 10/32