Binomial probability problem solving. The probability of sales representative making a sale with any one customer is 1/3. The sales representative makes eight contacts a day. To find the probability of making four sales, evaluate the term 8C_4(1/3)^4(2/4)^4

Lustyku8 2022-09-24 Answered
Binomial probability problem solving
The probability of sales representative making a sale with any one customer is 1 3 . The sales representative makes eight contacts a day. To find the probability of making four sales, evaluate the term
8 C 4 ( 1 3 ) 4 ( 2 4 ) 4
In the expansion ( 1 3 + 2 3 ) 8
I know how to evaluate 8 C 4 ( 1 3 ) 4 ( 2 4 ) 4 but I don't understand what they mean by " in the expansion of ( 1 3 + 2 3 ) 8
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Answers (1)

embraci4i
Answered 2022-09-25 Author has 10 answers
Step 1
The binomial theorem is that for variables a,b and positive integer exponent n, then we have the following.
( a + b ) n = k = 0 n n C k a k b n k
Since 1 = ( 1 3 + 2 3 ) 8 , then the term for k = 4 corresponds to the probability of 4 successes and 4 failures among 8 independent trials.
1 = k = 0 8 P ( X = k )
Step 2
Therefore,
P ( X = 4 )   =   8 C 4 1 3 4 2 3 4
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