Question

There are 16 number-tiles in a jar, each marked with a different number from 1–16. If you pull out one tile at random, what is the probability that the number you pull will be an even number or an odd prime number?

Answer 1

Please help me understand how to solve this problem.

Answer 2

How many even numbers are there from 1 to 16?
How many numbers are odd prime numbers from 1 to 16?

Answer 3

They're mutually exclusive, so just find the probability of each outcome and add them up.

Answer 4

Mutually exclusive means\[
\Pr(A\cap B)=0
\]In this case it helps because \[
\Pr(A\cup B) = \Pr(A)+\Pr(B)-\Pr(A\cap B) = \Pr(A)+\Pr(B)
\]

Answer 5

@mathstudent55 There are 8 even numbers (2,4,6,8,10,12,14,16) and 8 odd prime numbers (1,3,5,7,9,11,13,15.)

Answer 6

Not all odd numbers are prime.

Answer 7

Sorry! 15 is not a prime and 1 isn't considered one, right? ...so 6 odd prime numbers?

Answer 8

The prime numbers from 1 to 16 are 3, 5, 7, 11, 13
There are 5 prime numbers from 1 to 16.

Answer 9

1 is not prime and 9 isn't either.

Answer 10

Because 9 is divided by 3... Okay. I apologize.

Answer 11

So, 5 and 8 is 13. And my total is 16.

Answer 12

No need to apologize. I'm glad you understood it.
Now, how many outcomes that we want are there? The number of even numbers plus the number of odd primes. That is 8 + 5 = 13.
Here they are listed:
2, 4, 6, 8, 10, 12, 14, 16, 3, 5, 7, 11, 13

Answer 13

Right, so the probability you pick one of these numbers is 13/16
the number of desired outcomes divided by the number of total outcomes

Answer 14

That was pretty simple. Would it be my final answer then?

Answer 15

Yes, the final answer is 13/16

Answer 16

Thank you so much! I appreciate you taking the time to help me understand how to solve this problem!

Answer 17

You are welcome.