Hints and solutions to
Make a List #8
Two different prime numbers are selected at random from the first ten
prime
numbers. What is the probability that the sum of the two primes is 24?
-
The first thing we need is a list of the first ten prime
numbers:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29
-
If we take order into account (so we consider choosing 3 and then 17
as being
different from choosing 17 and then 3), then there are 10 ways to pick
the first number
and 9 ways to pick the second, for a total of 90 ways to pick two numbers
at random.
-
Now we have to see how many of these 90 ways give us a sum of 24. In
order to be
systematic, we'll list the possibilities in increasing order of the first
number.
-
Well, there's 5+19, 7+17, 11+13, 13+11, 17+7 and 19+5.
-
So 6 of the 90 possibilities give us a sum of 24. We conclude that
the probability
of getting a sum of 24 is 6/90 =
1/15.