Question

A coin is tossed 12 times. What is the probability of getting exactly 6 tails?

What is the probability of getting 6 consecutive tails?

Answer 1

The probability is `P=924/4096~~0.2256`.

Explanation:

Let `P` be the probability of getting exactly `6` tails, when a coin is tossed `12` times.

Now let us consider the following:

1. probability of success from one toss be `color(red)(p)`.

2. probability of failure from one toss be `color(red)(q)`.

3. number of trials be `color(red)(n)`.

4. number of success be `color(red)(r)`.

5. number of failures is `color(red)(n-r)`.

Hence, the total probability of succeeding is represented by `rarr`

`color(red)(P=nC_(r)p^(r)q^(r-x))`.......(1).

Here,

`p=q=1/2`

`n=12` `larr` Given.

`r=6` `larr` Given.

`:.n-r=6`

Now, substituting this into (1), we get

`P=""_12C_6(1/2)^6(1/2)^6`
`color(white)P=(12!)/(6!(12-6)!)*1/2^12`
`color(white)P=924*1/4096`
`color(white)P~~0.2256`

Hope it Helps :)