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customers of a hardware shop make a payment either in cash or with credit/debit card with probabilities 0.3 and 0.7, respectively. assume these probabilities apply to all customers independently. if 20 customers pay at the hardware shop, what is the probability that exactly 5 customers pay in cash?



Answer :

probability that exactly 5  customers pay in cash  is 0.178863

Total number of customer = 20

probability of payment in cash = 0.3

probability of payments via other methods  = 1 - 0.3 =0.7

let probability of payment in cash be p

and probability of payments via other methods be q

To find the probability that exactly y customers pay in cash

p [ x = y ] =  [tex]n_c__x p^x q ^(n-x)[/tex]

here value of y= 5 and n=20 , p =0.3 , q= 0.7

putting the values in above equations we get:

p [ x =5 ] = [tex]20_c__5 * 0.3 ^5 * 0.7 ^15[/tex]

p [ x =5 ] = (15504) * (0.00243) * (0.0047475615)

p [ x =5 ] = 0.178863

so the probability that exactly 5  customers pay in cash  is 0.178863

To know more about probablility click on below link:

https://brainly.com/question/1305783#

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