Question

A coin is tossed 7 times. What is the probability that the number of heads obtained will be 6? Express your answer as a fraction or a decimal number rounded to four decimal places.

Answer 1

Solution:

Consider a experiment of tossing a coin.

There are two possible outcomes.

S = { Head , Tail }

Let p be the probability of success of an event of HEAD

p = 1/2 = 0.5

A coin is tossed 7 times.

n = 7

Let X be the number of heads

X follows Binomial(7 , 0.5)

Using binomial probability formula ,

P(X = x) = (_n C _x) * p^x * (1 - p)^{n - x} ; x = 0 ,1 , 2 , ....., n

P(number of heads obtained will be 6)

= P(X = 6)

= (₇ C ₆) * 0.5⁶ * (0.5)^{7 - 6}

= {7!/6!*1! } * (1/2)⁶ (1/2)¹

= 7 /2⁷

= 7/128

= 0.0547

P(number of heads obtained will be 6) = 7/128 = 0.0547