A fair coin is flipped 3 times. The probability of getting exactly two heads, given that at least one flip results in a head, can be written as a/b, where a and b are coprime positive integers. What is the value of a+b?
please answer
its urgent
10
10 looks good to me.
Of the 8 possible outcomes, 7 have at least one head
3 of those have exactly 2 heads.
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To find the probability of getting exactly two heads, given that at least one flip results in a head, we need to consider the sample space and the favorable outcomes.
Let's start by considering the sample space, which represents all possible outcomes. When flipping a fair coin 3 times, there are 2 possible outcomes for each flip: heads (H) or tails (T). Therefore, the sample space consists of 2^3 = 8 possible outcomes:
HHH, HHT, HTH, THH, HTT, THT, TTH, TTT
Out of these 8 outcomes, we need to determine the number of favorable outcomes – those that have exactly two heads and at least one head. Let's list these outcomes:
HHH (does not meet the condition of at least one head)
HHT
HTH
THH
So, there are 3 favorable outcomes.
Now, we can calculate the probability by dividing the number of favorable outcomes by the total number of outcomes. Therefore, the probability of getting exactly two heads, given that at least one flip results in a head, is 3/7.
Since 3 and 7 are coprime positive integers, the sum of a and b is a + b = 3 + 7 = 10.
Therefore, the value of a + b is 10.