Question

When Jerome plays darts. The chances they hit the bulls eye is 1/2 .   (This was the question before the one below)

a)Draw a Tree diagram to represent the problem when three darts are thrown.

b)What is the probability three darts in a row hit the bullseye?

c)What is the probability that none of the three hit the bullseye?

d)What is the probability at least one of the three will hit the bullseye?

e)What is the probability exactly 2 of the three hit the bullseye?

When Jerome improves his game of darts the chances that a she hits a bullseye  is 3/5. Assume that each throw is independent.

a)What is the probability three darts in a row hit the bullseye?

b)What is the probability that none of the three hit the bullseye?

c)What is the probability at least one of the three will hit the bullseye?

d)What is the probability exactly 2 of the three hit the bullseye?

Answer 1

Here P(Hit the bulls eye) = 1/2

(a) We throw three darts. Here hit is H and no Hit is NH.

(b) P(Three darts in a row hits the bullseye) = 1/8 (as there is one HHH out of 8 options)

(c) P(None of these hits the bullseye) = 1/8

(d) P(Exactly two hits the bullseys) = {HHNH, HNHH, NHHH) = 3/8

Here new probability of success = 3/5

(a) probability three darts in a row hit the bullseye = 3/5 * 3/5 * 3/5 = 27/125

(b) P(None of three darts in a row hit the bullseye) = 2/5 * 2/5 * 2/5 = 8/125

(c) P(At least one of the three will hit the bullseye) = 1 - P(No hits the bullsyes) = 1 - 8/125 = 117/125

(d) P(Exactly two hits the bulls eye) = 3/5 * 3/5 * 2/5 + 3/5 * 2/5 * 3/5 + 2/5 * 3/5 * 3/5 = 54/125