When Ayla plays that's the chances that a she hit a bulls eye is 0.5.
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
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.
A) To draw a tree diagram, we will start by representing the first dart throw. There are two possible outcomes - a hit (H) or a miss (M). Then, for each outcome, we will draw branches representing the second dart throw, with the same two possible outcomes. We repeat this process for the third dart throw as well. The final diagram will look like:
H M
/ \ / \
H M H M
/ \ / \ / \ / \
H M H M H M H M
B) To find the probability that three darts fired in succession will all hit the bullseye, we need to multiply the probability of hitting each time. Since the probability of hitting the bullseye is 0.5 for each dart, the probability of hitting three times in a row is:
0.5 * 0.5 * 0.5 = 0.125
So, the chances that three darts fired in succession will all hit the bullseye is 0.125 (or 12.5%).
C) To find the probability that none of the darts will hit, we need to find the probability of a miss (M) for each dart and multiply them together. Since the probability of missing the bullseye is 0.5 for each dart, the probability that none will hit is:
0.5 * 0.5 * 0.5 = 0.125
So, the probability that none of the darts will hit is 0.125 (or 12.5%).
D) To find the probability that at least one dart will hit, we can subtract the probability that none of the darts will hit from 1. So, the probability that at least one will hit is:
1 - 0.125 = 0.875
So, the probability that at least one dart will hit is 0.875 (or 87.5%).
E) The given information does not provide any details about your probability of hitting.