You read 8 plays over 2 days, 4 plays per day.

If Hamlet and Macbeth are two plays, what is the probability that you read them on the same day?

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- Jan 30th 2007, 07:08 AMthefirsthokageBook Reading
You read 8 plays over 2 days, 4 plays per day.

If Hamlet and Macbeth are two plays, what is the probability that you read them on the same day? - Jan 30th 2007, 12:15 PMSoroban
Hello, thefirsthokage!

Here's one approach . . .

Quote:

You read 8 plays over 2 days, 4 plays per day.

If Hamlet and Macbeth are two of the plays,

what is the probability that you read them on the same day?

There are: $\displaystyle \binom{8}{4,4} = 70$ ways to read the books.

There are two cases to consider:

If you read Hamlet and Macbeth on the first day,

. . there are $\displaystyle \binom{6}{2} = 15$ choices for the other 2 books read the first day.

. . The other 4 books are read the second day.

If you read Hamlet and Macbeth on the second day,

. . there are $\displaystyle \binom{6}{2} = 15$ choices for the other 2 books read the second day.

. . The other 4 books are read the first day.

Hence, there are $\displaystyle 15 + 15 \:=\:30$ ways that Hamlet and Macbeth can be read on the same day.

Therefore: $\displaystyle P(\text{Hamlet \& Macbeth, same day}) \:=\:\frac{30}{70} \:=\:\frac{3}{7}$

- Jan 30th 2007, 12:34 PMCaptainBlack
Prob H read on day1 is 4/8, prob M read on day 1 given that H read on day 1

is 3/7. Therefore prob both read on day 1 is (4/8)(3/7)~=0.214.

(that is there are 4 slots out of 8 which are on day 1 to read H, but once

H is allocated to a slot on day 1 there remain 7 slots of which 3 are on

day 1 available for M.)

The prob that they are both read on dy 2 is the same, so the prob that they

are read on the same day is ~=2x0.214=0.428

RonL