Final answer:
To find the probability that Lenny will lie twice in his next 7 statements, we can use the binomial probability formula.
Thus, the probability that Lenny will lie twice in his next 7 statements is 0.344.
Step-by-step explanation:
To find the probability that Lenny will lie twice in his next 7 statements, we can use the binomial probability formula. The formula is:
P(X=k) = C(n,k) * p^k * (1-p)^(n-k)
Where:
P(X=k) is the probability of getting k successful outcomes,
C(n,k) is the number of ways of choosing k successes out of n trials,
p is the probability of getting a successful outcome in a single trial, and
n is the total number of trials.
In this case, the probability that Lenny is lying is 0.38, so p = 0.38. The number of trials is 7, so n = 7. We want to find the probability of lying twice, so k = 2.
Plugging these values into the formula, we get:
P(X=2) = C(7,2) * 0.38^2 * (1-0.38)^(7-2) = 0.344
Therefore, the probability that Lenny will lie twice in his next 7 statements is 0.344.