Question

There are five multiple choice questions asked in an exam. There is a chance of 70% that Shreya will solve a question correctly. Let X be the random variable that represents the number of questions she solves correctly. Which of the following is the probability mass function of X? (Assume that the correctness of answers to different questions are independent)

Answer 1

Given : There are five multiple choice questions asked in an exam.

There is a chance of 70% that Shreya will solve a question correctly.

Let X be the random variable that represents the number of questions she solves correctly.

(Assume that the correctness of answers to different questions are independent)

To Find :   the probability mass function of X

Solution:

p = 0.7  

q = 1 - p = 1 - 0.7 = 0.3

n = 5

X  = x  from 0 to 5

P(X)  = ⁿCₓpˣqⁿ⁻ˣ

P(0)  = ⁵C₀(0.7)⁰(0.3)⁵  = 0.00243

P(1)  = ⁵C₁(0.7)¹(0.3)⁴  =  0.02835

P(2)  = ⁵C₂(0.7)²(0.3)³  = 0.1323

P(3)  = ⁵C₃(0.7)³(0.3)²  = 0.3087

P(4)  = ⁵C₄(0.7)⁴(0.3)¹  = 0.36015

P(5)  = ⁵C₅(0.7)⁵(0.3)⁰  = 0.16807

Probability mass function is attached

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