Question

There are 10 kids out of 48 in a class that walk to school. If you randomly select 4 students, what is the probability that all 4 walk to school? Round to the nearest thousandths.

Answer 1

The probability of randomly selecting 4 students who walk to school out of a class of 48, where 10 kids walk to school, is approximately 0.001 when rounded to the nearest thousandths.

Step-by-step explanation:

The probability that all 4 students selected from a class randomly walk to school when 10 out of 48 kids walk to school can be found using combinations. First, calculate the number of ways to choose 4 walkers from the 10 walking students. This can be done using the combination formula C(n, k) = n! / (k!(n-k)!), where n is the total number of items to choose from, and k is the number of items to choose.

There are C(10, 4) ways to choose 4 walkers, which is 10! / (4!(10-4)!) = 210 ways. Then calculate the total number of ways to choose any 4 students from the entire class of 48. This is C(48, 4) = 48! / (4!(48-4)!) = 194,580 ways.

The probability of choosing 4 walking students is therefore the number of ways to choose 4 walkers divided by the total number of ways to choose 4 students: P(4 walkers) = 210 / 194,580. This gives us a probability of approximately 0.001 (rounded to the nearest thousandths).