What is the probability of obtaining exactly two heads in three flips of a coin, given that at least one is a head?
To find the probability of obtaining exactly two heads in three flips of a coin, given that at least one is a head, we need to use conditional probability.
First, let's calculate the total number of possible outcomes when flipping a coin three times. Since each flip has two possible outcomes (head or tail), the total number of outcomes is 2 * 2 * 2 = 8.
Next, let's calculate the number of favorable outcomes, which is the number of ways we can get exactly two heads in three flips, given that at least one is a head.
To do this, we can break down the problem into cases:
Case 1: Getting two heads and one tail
- The possible outcomes can be HHT, HTH, or THH.
Case 2: Getting three heads
- The possible outcome is HHH.
Therefore, there are four favorable outcomes: HHT, HTH, THH, and HHH.
Now, since we are given that at least one flip results in a head, we need to consider only the favorable outcomes that have at least one head. This excludes the outcome TTT.
Out of the four favorable outcomes, three have at least one head: HHT, HTH, and HHH.
Finally, the probability of obtaining exactly two heads in three flips of a coin, given that at least one is a head, is found by taking the number of favorable outcomes with at least one head divided by the total number of possible outcomes:
P(2 heads | at least 1 head) = 3/8
Therefore, the probability is 3/8 or 0.375, which can be expressed as a percentage as 37.5%.