SOLUTION: Let the random variable x represent the number of automobiles that a top salesperson will sell to a corporate client. The only possible values for are 0, 1 and 2, and the probabil

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Question 945652: Let the random variable x represent the number of automobiles that a top salesperson will sell to a corporate client. The only possible values for are 0, 1 and 2, and the probabilities for each of these values may be calculated from the formula
P(x)=0.5-(x/6) where x=0, 1 or 2
What is the probability that a randomly selected top salesperson will sell
i. at least 1 automobile to a corporate client?
ii. at most 1 automobile to a corporate client?
iii. exactly 1 automobile to a corporate client?
 

Answer by mathmate(429) About Me  (Show Source):
You can put this solution on YOUR website!

Given
P%28X%29=0.5-%28X%2F6%29 with X∈{0,1,2}

Find
1. P(X≥1)
2. P(X≤1)
3. P(1)

Solution

Using the given probability distribution, we find
P(0) = 0.5-0%2F6+=+1%2F2
P(1) = 0.5-1%2F6+=+1%2F3
P(2) = 0.5-2%2F6+=+1%2F6
from which we check ΣP(X)=1%2F2%2B1%2F3%2B1%2F6+=+1 checks.

Since the probabilities are mutually exclusive, we can apply the addition rule:
1. P(X≥1) = P%281%29%2BP%282%29+=+1%2F2
2. P(X≤1) = P%280%29%2BP%281%29+=+5%2F6
3. P(1) = 1%2F3