The probability that a student uses the Academic Resource Center on a regular basis is 0.43 . In a group of 21 students, what is the probability that exactly 4 of them use the Academic Resource Center on a regular basis?
To find the probability of exactly 4 students out of 21 using the Academic Resource Center on a regular basis, we can use the binomial probability formula.
The binomial probability formula is:
P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)
Where:
P(X = k) is the probability of exactly k successes
C(n, k) is the number of combinations of n items taken k at a time
p is the probability of success for a single event
(1 - p) is the probability of failure for a single event
n is the total number of trials/experiments/events
In this case, we want to find P(X = 4), the probability of exactly 4 students out of 21 using the Academic Resource Center on a regular basis.
Using the formula:
P(X = 4) = C(21, 4) * 0.43^4 * (1 - 0.43)^(21 - 4)
Calculating the combinations:
C(21, 4) = 21! / (4! * (21 - 4)!)
= 21! / (4! * 17!)
Calculating the probability:
P(X = 4) = (21! / (4! * 17!)) * 0.43^4 * (1 - 0.43)^(21 - 4)
Calculating this expression will give you the probability that exactly 4 students out of 21 use the Academic Resource Center on a regular basis.