Question

When Ayla improves her game of darts the chances that a she hits a bullseye is 0.65.
Assume that each throw is independent.

Answer 1

a) What are the chances that three darts fired in succession will all hit bullseye?

b) What is the probability that none will hit?

c) What is the probability that at least one will hit?

d) What is the probability that 2 will hit?

Answer 2

probability of hitting a bulls-eye = 0.65

probability of not hitting a bulls-eye = 1 - 0.65 = 0.35

with that said:

part a) all three bulls-eyes: 0.65 multiplied by itself three times, or 0.65*0.65*0.65

part b) same logic as part a) but using the probability of a miss

part c) "at least one will hit" this is the exact opposite of the event in part b). so you can take 1 - the probability from part b

part d) the probability that two will hit

you have three ways this could happen:
Miss-Hit-Hit
Hit-Miss-Hit
Hit-Hit-Miss

alll three of these have the same probability. calculate the probability of miss-hit-hit using the same logic we've been using so far, then multiply by 3