Final answer:
To find the probability of getting heads exactly 6 times when it is known that heads occur at least three times, we need to consider the total number of possible outcomes. First, find the number of outcomes where heads occur exactly 6 times. Then, find the number of outcomes where heads occur at least three times. Finally, divide the number of outcomes with heads occurring exactly 6 times by the number of outcomes with heads occurring at least three times.
Step-by-step explanation:
To find the probability of getting heads exactly 6 times when it is known that heads occur at least three times, we need to consider the total number of possible outcomes that have heads occurring at least three times.
First, let's find the number of outcomes where heads occur exactly 6 times. Since a fair coin is flipped 6 times, the total number of outcomes is 2^6 = 64.
Next, we need to find the number of outcomes where heads occur at least three times. This can be calculated by subtracting the number of outcomes where heads occur less than three times from the total number of outcomes. The number of outcomes where heads occur less than three times is the sum of the outcomes where heads occur 0, 1, or 2 times.
The probability of getting heads exactly 6 times when it is known that heads occur at least three times is the number of outcomes where heads occur exactly 6 times divided by the number of outcomes where heads occur at least three times, which is (number of outcomes with heads occurring exactly 6 times)/(number of outcomes with heads occurring at least three times).