Question 1196340
<br>
I always strongly recommend to students who are studying probability that they become familiar with Pascal's Triangle, because it is often a very useful tool in solving problems like this.  And for problems involving flipping a fair coin, it is especially useful.<br>
The 5th row of Pascal's Triangle is<br>
1, 5, 10, 10, 5, 1<br>
Those numbers are, respectively, C(5,5), C(5,4), ..., C(5,1), and C(5,0).<br>
Since this problem is about flipping a fair coin, we can think of the numbers in the 5th row of Pascal's Triangle as the probabilities of getting each different number of heads in 5 flips:<br><pre>
number of heads:   5     4      3      2     1     0
probability:      1/32, 5/32, 10/32, 10/32, 5/32, 1/32</pre>
This problem asks for the probability that the number of heads in 5 flips is a prime number -- 2, 3, or 5.  So add the probabilities for those numbers of heads to get the answer: 10/32 + 10/32 + 1/32<br>
ANSWER: 21/32<br>