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

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ANSWER


P\text{ = }(400)/(823543)

Step-by-step 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) = }(2)/(7)\cdot\text{ }(2)/(7)\cdot\text{ }(2)/(7)\cdot\text{ }(2)/(7)\cdot\text{ }(5)/(7)\cdot\text{ }(5)/(7) \\ P\text{ = }(400)/(823543) \end{gathered}

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

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