Answer to Question #122418 in Statistics and Probability for sarmad naveed

Question

Find the probability that a person tossing 3 coins will get either all heads or all tails for the second time on the fifth toss?



Select one:
a. 0.1069
b. 0.105
c. 0.256

Answer 1

Number of sample spaces when 3 coins tossed= 8

P(getting all heads or all tails )= 2/8=1/4

To find : probability of occurring all heads or all tails in tosses 1-4 and then again on toss 5

solution: Let x be the number of trials until get either all heads or all tails for the second time , the x is a negative binomial random variable.

Formula:

$b(x;k,p)=\binom{x-1}{k-1})p^{k}q^{x-k},$

x= k , k+1,k+2,.....k=2

P(x=5)=b(5;2,1/4)=$\binom{4}{1}$ (1/4)²(3/4)³=27/256=0.105

Answer: 0.105