Question
Question: The probability that Dhoni will hit a century in every ODI match he lays is . If he plays matches in...
The probability that Dhoni will hit a century in every ODI match he lays is . If he plays matches in World Cup 2011 , the probability that he will score century in all the test matches is :51
A 31251
B 31255
C 156254096
D 31251555
Solution
In this question use the Bernoulli's trials , So from Bernoulli trial Probability = nCrprqn−r where n is number of trial and r will be the success getting out of n hence for this n = 6 r=6 p=51 q=54 from this we will proceed towards answer .
Complete step-by-step answer:
As in the given question the probability that Dhoni will hit century in every ODI matches , is 51 we have to find that the probability that he will score century in all the 6 test matches ,
So the probability of getting a century , p=51
Probability of not getting a century , q=54
And it is given that the total number of matches is 6
So in this we use Bernoulli's trials as
Bernoulli trials approaches the probability of success as the number of trials increases towards infinity ,
So from Bernoulli trial
Probability = nCrprqn−r where n is number of trial and r will be the success getting out off n ,
In this case n = 6 because 6 test matches is played and out which we want success in all so r=6
And from above we know that the p=51 and q=54 so on putting these values in Bernoulli trial
Probability that he will hit century in all matches is = 6C6(51)6(54)6−6
we know that the value of 6C6=1 and 56=3125 on solving ,
Probability = 31251
Probability that he will score century in all the 6 test matches is 31251 hence Option A is correct .
Note: If in this question it will asked that the probability he will not score century in all the 6 test matches then we will use Probability of unsuccessful event = 1− Probability of successful event , and Probability of successful event = 31251 or we will also put in nCrprqn−r r=0 in this equation .