Question

A class has six students. What is the probability that exactly four of the students were born on a weekend?

Answer 1

ANSWER

$P\text{ = }\frac{400}{823543}$

EXPLANATION

There are six students in the class.

There are 7 days in a week. There are 2 days in the weekend. There are 5 weekdays.

The probability that any student is born on the weekend is given as:

P(weekend) = 2/7

The probability of being born on a weekday is:

P(weekday) = 5/7

Now the probability that 4 out of the six students is born on a weekend will be given as the products of four of them born on a weekend and the remaining two born on a week day:

$\begin{gathered} P(4\text{ are born on a weekend) = }\frac{2}{7}\cdot\text{ }\frac{2}{7}\cdot\text{ }\frac{2}{7}\cdot\text{ }\frac{2}{7}\cdot\text{ }\frac{5}{7}\cdot\text{ }\frac{5}{7} \\ P\text{ = }\frac{400}{823543} \end{gathered}$

That is the probability that 4 out of 6 of them are born on a weekend.