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

What is the probability of getting 6 consecutive tails?

1 Answer
Oct 16, 2017

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 :)