Answer :

Given that, obtaining multiple of 3 in a throw of a die is a success.


There are total 10 throws of a fair die.


Let p be the probability of getting multiple of 3 in a throw of a die.


Since there can be a total 6 outcomes in a throw of a die. That is, {1, 2, 3, 4, 5, 6}.


And a multiple of 3 in a die is {3}, {6}.




Then, let q be the probability of not getting a multiple of 3 in a throw of a die.


And we know, p + q = 1


q = 1 – p





Let X be a random variable representing a number of successes (getting multiple of 3 in die) out of 10 throws of a die.


Then, the probability of getting r successes out of n throws of die is given by,


P (X = r) = nCrprqn-r


Here n = 10.


Now, put values of n, p, and q in the above equation.


…(i)


We need to find the probability of getting a multiple of 3 in at least 8 of the throws out of 10 throws of a fair die.


It is given,


Probability = P (X ≥ 8)


This can be written as,


P (X ≥ 8) = P (X = 8) + P (X = 9) + P (X = 10)


Just out r = 8, 9, 10 in equation (i) to find the value of P (X = 8), P (X = 9), P (X = 10) respectively, then substitute in the above equation.










Thus, the probability of getting a multiple of 3 in at least 8 of the throws out of 10 throws of a fair die is 201/310.


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses
RELATED QUESTIONS :

A box has 100 penMathematics - Exemplar

State True or FalMathematics - Exemplar

A random variableMathematics - Board Papers

How many times muMathematics - Board Papers

A card from a pacMathematics - Board Papers

An experiment sucMathematics - Board Papers

A bag A contains Mathematics - Board Papers

On a multiple choMathematics - Board Papers

Mark the correct RD Sharma - Volume 2