Question

Jillian plays darts professionally. Suppose that she has a \[20\%\] probability of hitting the when she aims for it in any given throw. Jillian is going to attempt \[2\] throws at the bullseye. We can categorize each throw as hitting the bullseye (B) or not (N). Here is a sample space showing the possible outcomes: \[1^\text{st}\] throw \[2^\text{nd}\] throw N N N B B N B B Which graph represents the theoretical probability distribution of the number of bullseyes?

Answer 1

The graph representing the theoretical probability distribution of the number of bullseyes is:

Number of bullseyes (X) Probability (P)

0 0.64

1 0.32

2 0.04

Here's how to calculate the probabilities:

No bullseyes (0): This happens when both throws result in a miss (N). The probability of this event is 0.8 * 0.8 = 0.64.

One bullseye (1): This can happen in two ways: either the first throw hits the bullseye and the second one misses (BN) or the second throw hits the bullseye and the first one misses (NB). The probability of each of these events is 0.2 * 0.8 = 0.16. The total probability of getting one bullseye is the sum of these probabilities, which is 0.16 + 0.16 = 0.32.

Two bullseyes (2): This happens only when both throws hit the bullseye (BB). The probability of this event is 0.2 * 0.2 = 0.04.

The graph shows that there is a 64% chance of getting no bullseyes, a 32% chance of getting one bullseye, and a 4% chance of getting two bullseyes.