The probability that you make an online sale is 0.30. If you talks to five customers, what is the probability that you will make exactly 2 online sales? (Assume independence.)
Question
The probability that you make an online sale is 0.30. If you talks to five customers, what is the probability that you will make exactly 2 online sales? (Assume independence.)
Solution
To solve this problem, we can use the binomial probability formula, which is:
P(X=k) = C(n, k) * (p^k) * ((1-p)^(n-k))
where:
- P(X=k) is the probability of k successes in n trials
- C(n, k) is the combination of n items taken k at a time
- p is the probability of success on a single trial
- n is the number of trials
- k is the number of successes
In this case, we have:
- n = 5 (the number of customers you talk to)
- k = 2 (the number of sales you want to make)
- p = 0.30 (the probability of making a sale)
First, calculate C(n, k). The formula for combinations is:
C(n, k) = n! / [k!(n-k)!]
where "!" denotes factorial, which means multiplying all positive integers up to that number. So, we have:
C(5, 2) = 5! / [2!(5-2)!] = (54321) / [(21)(321)] = 10
Next, calculate p^k and (1-p)^(n-k):
p^k = (0.30)^2 = 0.09 (1-p)^(n-k) = (1-0.30)^(5-2) = (0.70)^3 = 0.343
Finally, substitute these values into the binomial probability formula:
P(X=2) = C(5, 2) * (0.30^2) * ((1-0.30)^(5-2)) = 10 * 0.09 * 0.343 = 0.309
So, the probability that you will make exactly 2 online sales when you talk to 5 customers is approximately 0.309 or 30.9%.
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