When Ayla plays that's the chances that a she hit a bulls eye is 0.5.

Question

A) draw a tree diagram to represent this problem 13 darts are thrown.
B) what are the chances that three darts fired in succession Will all hit bulls eye?
C) what is the probability that none will hit
D) what is the probability that at least one will hit
E) what is the probability that you will hit

Answer 1

A) The tree diagram can be drawn as follows:

H (Hit Bulls Eye)
/
H - o
/ \
S - M (Miss Bulls Eye)
\ /
M - o
\
M

B) To find the chances that three darts fired in succession will all hit bulls eye, we multiply the probability of hitting bulls eye for each dart since the events are independent.

P(three darts hit) = P(hit) * P(hit) * P(hit)
= 0.5 * 0.5 * 0.5
= 0.125

The chances that three darts fired in succession will all hit bulls eye is 0.125 or 12.5%.

C) The probability that none of the darts will hit is calculated by multiplying the probability of missing bulls eye for each dart since the events are independent.

P(none hit) = P(miss) * P(miss) * P(miss)
= 0.5 * 0.5 * 0.5
= 0.125

The probability that none of the darts will hit is 0.125 or 12.5%.

D) The probability that at least one dart will hit is the complement of the probability that none will hit.

P(at least one hit) = 1 - P(none hit)
= 1 - 0.125
= 0.875

The probability that at least one dart will hit is 0.875 or 87.5%.

E) The probability that you will hit cannot be determined without knowledge of your own ability or the given probability of hitting bulls eye.