Each of the total fice questions in amultiple choice examination has four choices, only one of which is correct.A student is attempting to guess the amswer . The renadom varible X is the number of question answerred correctly. What is the probability that the student will giveat least one correct answer ?

Explanation

Let X = number of questions answered correctly
P = probability of giving correct answer
`therefore p= 1/4 `
`therefore q= 1 p=1- 1/4 = 3/4 `
Given : n= 5
` therefore X ~ B (5, 1/4)`
The p.m of on X is given as : `P [ X =x ]= ""^nC_x P^xq^(n-x)`
i.e `p(x) = ""^5C_x(1/4)^x(3/4)^(5-x)`
P(at least one correct answer)
`= P [ X ge 1] =1 - P[ X=0] `
`= 1-p(0)=1 - ""^5C_0(1/4)^0 (3/4)^(5-0)`
`1-1 xx (3/4) ^5 =1 - 243/1024 `
` = 781/ 1024`