Question

A coin is weighted so that there is a 63% chance that it will come up "heads" when flipped.

The coin is flipped four times. Find the probability of at least one of the flips resulting in "tails".

Round your answer to four decimal places.

Answer 1

Let , 'p' be the probability that it will come up "tails"

Here , p=1-the probability that it will come up "heads"=1-0.63=0.37

Since , the coin is flipped four times.

i.e. n=4

Let , X be the number of flips resulting in "tails"

The possible number of X are 0,1,2,3,4

Here , X has binomial distribution with parameter n=4 and p=0.37

Therefore , the probability mass function of X is ,

; x=0,1,2,........,n and q=1-p

= 0 ; otherwise

Now , we want to find the probability of at least one of the flips resulting in "tails"