Question

there are five people sat in a room and each chooses, at random, a number from 1 to 10. what is the probability that two or more people have exactly the same number?

Answer 1

The probability that two or more of the five people choosing a random number from 1 to 10 have the same number is approximately 69.76%.

Step-by-step explanation:

The question is asking for the probability that in a scenario where five people each choose a random number from 1 to 10, two or more people will select the exact same number. To calculate this, it's easiest to calculate the complement, the probability that all five people choose different numbers, and subtract it from 1 (which represents certainty).

First, the total number of ways the first person can choose a number is 10. The second person then has 9 remaining unique choices to avoid matching the first person, the third person has 8, and so on. The probability of all five people choosing unique numbers is calculated by multiplying these chances together and then dividing by 10^5 (since there are 10 choices for each of the 5 people).

P(All unique) = (10/10) * (9/10) * (8/10) * (7/10) * (6/10) = 0.3024

To find the probability of at least one match, we subtract this from 1: P(At least one match) = 1 - P(All unique) = 1 - 0.3024 = 0.6976, or approximately 69.76%.