Question

40 people play a game in which they have to choose an integer between 1 and 100 inclusive, independently of others. for a particular pair of people, what is the probability that they choose the same integer? show your work. 40 people play a game in which they have to choose an integer between 1 and 100 inclusive, independently of others. for a particular pair of people, what is the probability that they choose the same integer? show your work.

Answer 1

The probability that two people out of 40 will independently choose the same integer from 1 to 100 is 1 in 100, or 0.01.

Step-by-step explanation:

The question asks for the probability that two people out of 40 will choose the same integer from 1 to 100, independently of each other. We are looking to calculate the probability that both individuals make the same choice, assuming that each integer is chosen with equal likelihood.

To calculate this, we first consider the choice of the first person. They can choose any integer between 1 and 100, so we have 100 possibilities. For the second person to choose the same integer, they only have one option that will match the first person's choice, out of the 100 possible integers they can choose. Therefore, the probability that the second person picks the same integer as the first person is 1 in 100 or 0.01.

The formula to find this probability is:

P(both choose same integer) = 1/100