Question 1099443: Can someone please help me, I did the work but I’m unsure if I did it correctly. I got some strange answer for a) .00317 for b) .0976 c) .01807
Suppose a salesperson makes a sale on 25 percent of customers contacts. In a normal work week, the salesperson contacts 20 customers.
A. What is the probability that the salesperson will make no sales?
B. What is the probability that the salesperson will make at least two sales?
C. What is the probability that the salesperson will make two sales at most?
Answer by math_helper(2461)   (Show Source):
You can put this solution on YOUR website! Pr{sale} = 0.25
therefore, Pr{no sale} = 0.75 on any given call to a customer.
a) Pr(no sales in 20 calls) = {{[ 0.75^20 }}} = (approx)  (matches yours)
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b) Pr( 2 or more sales in 20 calls) = 1 - Pr (zero sales or one sale)
Pr(zero sales) = 0.00317 (from part(a))
Pr(1 sale) =  = 0.0211414
Pr(zero or 1 sale) = 0.00317 + 0.0211414 = 0.0243114
So Pr( 2 or more sales ) = 1 - 0.0243114 = 0.975688
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c) Pr ( 2 sales at most) = Pr(0 sales) + Pr(1 sale) + Pr(2 sales)
We have Pr(0 sales) and Pr(1 sale) already, just need to compute Pr(2 sales):
Pr(2 sales) =  = (approx) 0.06695
Pr( 2 sales at most) = 0.00317+0.0211414+0.06695 = 0.09126
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You may have forgotten to use C(n,r) in your calculations. This is needed because, for instance, when computing the probability of exactly one sale, (0.25)^1*(0.75)^19 only computes the probability that the first call is a sale and the remaining 19 calls are no-sales. Multiplying by C(20,1) accounts for the possible position of the one sale within the 20 calls. I hope this makes sense, below is a diagram showing why you must multiply by C(20,1) for the one-sale case:
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Using 1=sale and 0=no sale, here are the ways of making exactly 1 sale
10000 00000 00000 00000 <<< Sale on 1st call (0.25)*(0.75)^19
01000 00000 00000 00000 <<< Sale on 2nd call
00100 00000 00000 00000 <<< Sale on 3rd call
: : : :
00000 00000 00000 00001 <<< Sale on 20th call
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Similarly, if you want to compute for exactly r sales, multiply by C(20,r).
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