Burger and sandwich#2

Probability Level 3

Mr. Robert sells only burger and sandwich.

40 % 40\% of people choose burger, the rest choose sandwich.

Mr. Robert says " 40 % 40\% choose burger, so 60 % 60\% choose sandwich. Therefore 6 out of the next 10 customers should choose sandwich."

What is the probability that Mr. Robert is right?

Give your answer to 4 decimal places.


The answer is 0.2508.

Munem Shahriar by Munem Shahriar , 18, Bangladesh

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1 solution

Toby M
Sep 17, 2017

We can use the formula for binomial probability: n ! ( r ! ) ( n − r ) ! ∗ p r ∗ ( 1 − p ) n − r \frac{n!}{(r!)(n-r)!} * p^r * (1-p)^{n-r} , where in this problem, we have n = 10 n = 10 customers, p = 0.6 p = 0.6 probability of an individual customer choosing a sandwich, and r = 6 r = 6 customers choosing a sandwich.

Plugging in the numbers, we have 10 ! ( 6 ! ) ( 10 − 6 ) ! ∗ 0. 6 6 ∗ ( 1 − 0.6 ) 10 − 6 \frac{10!}{(6!)(10-6)!} * 0.6^6 *(1-0.6)^{10-6} , which is approximately 0.2508 0.2508 .

0 Helpful 0 Interesting 0 Brilliant 0 Confused

Thanks for posting a solution. You can use \approx in this case.

Which appear as, ≈ \approx

Munem Shahriar - 3 years, 8 months ago

Thanks for the comment, but I don't think I need to use it in this situation.

Toby M - 3 years, 8 months ago

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