Question

A coin is flipped 12 times. What is the probability of getting exactly 8 heads?

Answer 1

Probability of getting exactly 8 heads in tossing a coin 12 times is `495/4096.`

Explanation:

If a coin is tossed 12 times, the maximum probability of getting heads is 12.
But, 12 coin tosses leads to `2^12`, i.e. 4096 number of possible sequences of heads & tails.

Let E be an event of getting heads in tossing the coin and S be the sample space of maximum possibilities of getting heads. Then probability of the event E can be defined as,

`P(E)=(n(E))/(n(S)).` [Where, n represents number accordingly].

`:.P(E)=495/4096.` (answer).

NOTE: To know more about probability, please check into :
http://www.careerbless.com/aptitude/qa/probability_imp.php.

Answer 2

`495/4096`

Explanation:

The number of possible sequences of heads and tails in `12` coin tosses is:

`2^12 = 4096`

The number of ways that such a sequence could contain exactly `8` heads is the number of ways of choosing `8` out of `12`...

`((12),(8)) = (12!)/((8!)(4!)) = (12xx11xx10xx9)/(4xx3xx2xx1) = 495`

So the probability of exactly `8` heads in `12` coin tosses is:

`495/4096`