Question

Suppose you have an experiment where you flip a coin three times. You then count the number of heads. What is the probability distribution?

Answer 1

When flipping a fair coin three times, the probability distribution for the number of heads can be determined by calculating the probability of each possible outcome. The probability distribution is as follows: P(X=0) = 1/8, P(X=1) = 3/8, P(X=2) = 3/8, P(X=3) = 1/8.

Step-by-step explanation:

When flipping a fair coin three times, the probability distribution for the number of heads can be determined by calculating the probability of each possible outcome. Let's list all the possible outcomes and their associated probabilities:

1. 0 heads: There is only 1 outcome (TT) and its probability is 1/8.
2. 1 head: There are 3 outcomes (HT, TH, HT) and each has a probability of 3/8.
3. 2 heads: There are 3 outcomes (HH, HH, HH) and each has a probability of 3/8.
4. 3 heads: There is only 1 outcome (HHH) and its probability is 1/8.

So, the probability distribution for the number of heads is:
0 heads: P(X=0) = 1/8
1 head: P(X=1) = 3/8
2 heads: P(X=2) = 3/8
3 heads: P(X=3) = 1/8