Question

An unbiased coin is tossed n times. if the probability of getting 4 tails equals the probability of getting 7 tails, then the probability of getting two tails is:

Answer 1

then the probability of getting two tails is 28

Answer 2

Answer:

The probability of getting two tails is : $\frac{55}{2048}$

Step-by-step explanation:

Given : An unbiased coin is tossed n times. if the probability of getting 4 tails equals the probability of getting 7 tails.

To find : The probability of getting two tails is?

Solution :

The probability of getting k tails in n tosses  is

$\text{P(k tails)}=\frac{\text{Ways of choosing k positions out of n to be the tails}}{\text{Total number of possible outcomes}}$

$\text{P(k tails)}=\frac{\binom{n}{k}}{2^n}$

Now, We have given

P(4 tails) = P(7 tails)

$\binom{n}{4} =\binom{n}{7}$

$n=4+7$

$n=11$

So,

$\text{P(2 tails)}=\frac{\binom{11}{2}}{2^11}$

$\text{P(2 tails)}=\frac{55}{2048}$

Therefore, The probability of getting two tails is :  $\frac{55}{2048}$