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## Comment on

2 heads## You can also solve this

## That's not quite correct.

That's not quite correct.

Your equation only accounts for one of many possible cases. That is, your equation is for calculating the probability of Heads - Heads - Tails - Tails - Tails

You also need to consider other cases like:

- Tails - Heads - Heads - Tails - Tails

- Tails - Tails - Heads - Tails - Heads

- Tails - Tails - Tails - Heads - Heads

etc.

If you evaluate your equation (.9*.9*.1*.1*.1), you get 0.00081 (not 0.0081)

## Q.N.: A fair coin is to be

7⁄32

1⁄4

5⁄16

3⁄8

7⁄16

## Let's examine ONE case in

Let's examine ONE case in which we get exactly 3 heads: HHHTT

P(HHHTT) = (1/2)(1/2)(1/2)(1/2)(1/2) = 1/32

This, of course, is just ONE possible way to get exactly 3 heads.

Another possible outcome is HHTTH

Here, P(HHTTH) = (1/2)(1/2)(1/2)(1/2)(1/2) = 1/32

As you might guess, each possible outcome will have the same probability (1/32). So, the question becomes "In how many different ways can we get exactly 3 heads and 2 tails?"

In other words, in how many different ways can we arrange the letters HHHTT?

Well, we can apply the MISSISSIPPI rule (from the counting module) to see that the number of arrangements = 5!/(3!)(2!) = 10

So P(exactly 3 heads) = (1/32)(10) = 10/32 = 5/16

## Or we can also choose the

(n choose k)Xp^kX(1-p)^n-k

(5 choose 2)X0.9^2X0.1^3

10X0.81X0.001

0.0081

## That works too!

That works too!

## Thanks for the wonderful

## Thanks Deepak!

Thanks Deepak!

## Add a comment