If 3 coins are thrown, the probability to have exactly two heads is:

a) 3/8

b) 2/6

Explain.

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- Aug 4th 2006, 10:16 AMbret803 coins
If 3 coins are thrown, the probability to have exactly two heads is:

a) 3/8

b) 2/6

Explain. - Aug 4th 2006, 10:31 AMgalactus

Where p=q=.5

You could try expanding and looking at the binomial expansion. - Aug 5th 2006, 09:01 AMbret80
Is there an easier way to find out the answer, is it that hard?

- Aug 5th 2006, 09:13 AMgalactus
That isn't difficult.

It may look imposing if you don't understand the notation.

The number of ways to choose 2 out of 3 objects is 3.

You have

Enter in your probabilities of success and failure. If you flip a coin the probabilities are 50-50.

So, you have

Maybe I should've explained it this way to start with:

Throw the 3 coins. How many possible arrangements can you have?.

. Right?.

Let's list them:

HTT

HHH

TTT

HHT

THH

HTH

THT

TTH

Now, how many of those have**exactly 2**H's?.....3. See?. - Aug 5th 2006, 10:21 AMSoroban
Hello, Bret!

Here's yet another approach . . .

Quote:

If 3 coins are thrown, the probability to have exactly two heads is:

. . .

Explain.

Suppose we want the coins to turn up__in____that____order__.

Prob. that coin #1 is Heads:

Prob. that coin #2 is Heads:

Prob. that coin #3 is Tails:

Hence: .

Since the problem did*not*insist on a specific order of Heads and Tails,

. . there are__three__ways to get two Heads: .

Therefore: .

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

**A handy tip**

If there are coins, how can we list all the outcomes?

Since each coin can turn up in 2 ways, there are: outcomes.

Write . . . first half 's, the second half is.

. . .

. . .

Write . . . this time "change every two".

. . .

. . .

. . .

. . .

Write . . . this time "change every one" (alternate).

. . .

. . .

Write the three columns side-by-side:

. . .

. . . and we have the eight possible outcomes!

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Of course, this procedure works for 4 coins (16 outcomes)

. . and 5 coins (32 outcomes) . . . it just takes longer.