Question

The numbers 1 through 10 are put in one bag. The numbers 5 through 14 are put in another bag. When you pick one number from each bag, what is the probability you get the same number? Enter your answer as a fraction.

Answer 1

6/100=3/50

Explanation:

The first bag contains the numbers 1 through 10, which is a total of 10 numbers. The second bag contains the numbers 5 through 14, which is also a total of 10 numbers.

The probability of picking the same number from both bags is the number of ways of picking the same number divided by the total number of possible outcomes. There are 10 possible outcomes in each bag, so the total number of possible outcomes is 10 × 10 = 100.

To count the number of ways of picking the same number, we can simply count the number of numbers that appear in both bags. There are six numbers that appear in both bags: 5, 6, 7, 8, 9, and 10.

Therefore, the probability of picking the same number from both bags is:

6/100

Simplifying this fraction by dividing both the numerator and denominator by 2 yields:

3/50

So the probability of picking the same number from both bags is 3/50.