SOLUTION: I am a salesperson & I close on 70% of all my sales. If I call on 4 sales, what is the probability that I will close on 3 of the 4 sales?

Question 664071: I am a salesperson & I close on 70% of all my sales. If I call on 4 sales, what is the probability that I will close on 3 of the 4 sales?
Found 2 solutions by jim_thompson5910, Theo:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Use the binomial probability distribution formula P(X = k) = (n C k)*(p)^(k)*(1-p)^(n-k)

In this case, k = 3, n = 4 and p = 0.7

P(X = k) = (n C k)*(p)^(k)*(1-p)^(n-k)
P(X = 3) = (4 C 3)*(0.7)^(3)*(1-0.7)^(4-3)
P(X = 3) = (4 C 3)*(0.7)^(3)*(0.3)^(4-3)
P(X = 3) = (4)*(0.7)^(3)*(0.3)^1
P(X = 3) = (4)*(0.343)*(0.3)
P(X = 3) = 0.4116

So the probability is 0.4116, which is a 41.16% chance.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the probability that you will close on a sale is .7
if you call on 4 sales, the probability that you will close on exactly 3 of them is equal to C(4,3)*.7^3*.3^1 which is equal to .4116
all the probabilities are shown in the following table

x c(4,x) .7^x .3^(4-x) p(x) 0 1.00 1.00 0.0081 0.0081 1 4.00 0.70 0.027 0.0756 2 6.00 0.49 0.09 0.2646 3 4.00 0.34 0.3 0.4116 4 1.00 0.24 1 0.2401

c(4,x) is the combination formula for selecting x items out of 4.
.7^x is the probability of making a sale raised to the x power.
.3^(4-x) is the probability of not making a sale raised to the (4-x) power
p(x) is equal to c(4,x) * .7^x * .3^(4-x)
that's the probability of getting x out of 4.
your solution is getting 3 out of 4 sales to be successful.
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