A grocery store is having a promotion for a new brand of milk.Every gallon has a 20% chance of having a coupon for a free box of breakfast cereal under the cap. If Valeria buys 3 gallons of milk,what is the probability that exactly one of them will win her a free box of cereal?
3/5
To find the probability that exactly one out of the three gallons of milk will win Valeria a free box of cereal, we can use the binomial probability formula. The binomial probability formula is given by:
P(x) = C(n, x) * p^x * q^(n-x)
Where:
P(x) is the probability of getting exactly x successes,
C(n, x) is the number of ways to choose x successes out of n trials,
p is the probability of success on a single trial, and
q is the probability of failure on a single trial.
In this scenario, Valeria has three trials (buying three gallons of milk), and the probability of success (getting a coupon for a free box of cereal) on a single trial is 20% or 0.2. Therefore, the probability of failure on a single trial is 80% or 0.8.
Applying the formula, we have:
P(exactly one success) = C(3, 1) * (0.2)^1 * (0.8)^(3-1)
To calculate C(3, 1), which represents the number of ways to choose 1 success out of 3 trials, we can use the formula for combinations:
C(n, x) = n! / (x! * (n-x)!)
Applying this formula, we find:
C(3, 1) = 3! / (1! * (3-1)!) = 3
Substituting the values into the probability formula:
P(exactly one success) = 3 * (0.2)^1 * (0.8)^(3-1)
Calculating this expression:
P(exactly one success) = 3 * 0.2 * 0.64 = 0.384
Therefore, the probability that exactly one out of the three gallons of milk will win Valeria a free box of cereal is 0.384 or 38.4%.