(i) Probability of making 2 sales: Approximately 0.1209
(ii) Probability of making 8 sales: Approximately 0.1209
To find the probabilities of Jeremy making 2 sales and 8 sales, we can use the binomial probability formula:
P(X=k) = (nCk) * p^k * (1-p)^(n-k)
Where:
P(X=k) is the probability of exactly k successes
n is the number of trials or people approached
k is the number of successes or sales
p is the probability of success on each trial (probability of making a sale)
(nCk) is the binomial coefficient, which represents the number of ways to choose k successes from n trials
(i) Probability of making 2 sales:
n = 10 (number of people approached)
k = 2 (number of sales)
p = 0.4 (probability of making a sale)
P(X=2) = (10C2) * 0.4^2 * (1-0.4)^(10-2)
Using the binomial coefficient formula:
(10C2) = 10! / (2! * (10-2)!) = 45
P(X=2) = 45 * 0.4^2 * 0.6^8 = 0.1209
Therefore, the probability that Jeremy will make 2 sales is approximately 0.1209.
(ii) Probability of making 8 sales:
n = 10 (number of people approached)
k = 8 (number of sales)
p = 0.4 (probability of making a sale)
P(X=8) = (10C8) * 0.4^8 * (1-0.4)^(10-8)
Using the binomial coefficient formula:
(10C8) = 10! / (8! * (10-8)!) = 45
P(X=8) = 45 * 0.4^8 * 0.6^2 = 0.1209
Therefore, the probability that Jeremy will make 8 sales is also approximately 0.1209.