Question

A probability that in a family of five members exactly two members have birthday on Sunday is

Answer 1

Answer:

it's probability is

2/5

I think it helps you to find the answer

Answer 2

Explanation:

let probability that birthday is on sunday = p

let probability that birthday is  not on sunday = q

number of success = r

then

$p = \frac{1}{7}\\\\ q=1-p\\\\1-\frac{1}{7}= \frac{6}{7}$

here r = 2

thus , The probability is

$^n C_r p^rq^n^-^r\\\\^5 C_2(\frac{1}{7})^2(\frac{6}{7})^5^-^2\\\\\frac{5!}{2!3!}(\frac{1}{7})^2(\frac{6}{7})^3\\\\\frac{5\times 4}{2}\times \frac{6^3}{7^5}\\\\=\frac{10 \times 6^3}{7^5}$

hence , The probability that exactly two members have birthday on Sunday is $\frac{10 \times 6^3}{7^5}$

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