# A pair of dice is

Given : A die is tossed twice and ‘Getting a number greater than 4 ’ is considered a success.

To find : probability distribution of the number of successes and mean (𝓊) and variance (σ2)

Formula used :

Mean = E(X) =

Variance = E(X2) -

When a die is tossed 4 times,

Total possible outcomes = 62 = 36

Getting a doublet is considered as a success

The possible doublets are (1,1) , (2,2) , (3,3) , (4,4) , (5,5) , (6,6)

Let p be the probability of success,

p = =

q = 1 – p = 1 - =

q =

since the die is thrown 4 times, n = 4

x can take the values of 1,2,3,4

P(x) = nCx

P(0) = 4C0 =

P(1) = 4C1 = =

P(2) = 4C2 = =

P(3) = 4C3 = =

P(4) = 4C4 =

The probability distribution table is as follows,

Mean = E(X) = = x1P(x1) + x2P(x2) + x3P(x3) + x4P(x4) + x5P(x5)

Mean = E(X) = 0() + 1() + 2() + 3() + 4()

Mean = E(X) = 0 + + + + = = =

Mean = E(X) =

= =

E(X2) = = P(x1) + P(x2) + P(x3) + P(x4) + P(x5)

E(X2) = () + () + () + () + ()

E(X2) = 0 + + + + = =

E(X2) = 1

Variance = E(X2) - = 1 – =

Variance = E(X2) - =

The probability distribution table is as follows,

Mean =

Variance =

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
view all courses
RELATED QUESTIONS :

An urn contains 3Mathematics - Board Papers

Two cards are draMathematics - Board Papers

There are three cMathematics - Board Papers

Three numbers areMathematics - Board Papers

Let <span lang="EMathematics - Board Papers

Which of the follRD Sharma - Volume 2

Which of the follRD Sharma - Volume 2

A random variableRD Sharma - Volume 2