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eLitmus Probability questions for eLitmus exam | eLitmus Questions for pH Test

26

A deck of 5 cards (each carrying a distinct number from 1 to 5) is shuffled thoroughly. Two cards are then removed one at time from the deck. What is the probability that the two cards are selected with the number on the first card being one higher than the number on the second card?

A.

1/5

B.

4/25

C.

1/4

D.

2/5

See Answer & Explanation Lets Discuss
Correct answer is : A
Explanation

So there are 5P2 = 5!/3! = 20 elementary events, as 5 cards can be arranged in 5P2 .

out of which there are 4 favorable number of cases:
1)5 before 4, 2)4 before 3, 3)3 before 2 and 4)2 before 1.
So, probability = 4/20 = 1/5

 
27

Consider a company that assembles computers. The probability of a faulty assembly of any computer is p. The company therefore subjects each computer to a testing process.This testing process gives the correct result for any computer with a probability of q. What is the probability of a computer being declared faulty?

A.

pq + (1 – p)(1 – q)

B.

(1 – q) p

C.

(1 – p) q

D.

pq

See Answer & Explanation Lets Discuss
Correct answer is : A
Explanation
A computer can be declared faulty in two cases
1) It is actually faulty and correctly declared, so  the probability =(p*q)
2) Not faulty and incorrectly declared, so the probability =(1-p)*(1-q)
 the probability of a computer being declared faulty= (p*q)+(1-p)*(1-q)
 
28

We are given a set X = {x1, …. xn} where xi = 2i. A sample S ⊆ X is drawn by selecting each xi independently with probability p1 = 1/2. The expected value of the smallest number in sample S is:

A.

1/n

B.

2

C.

sqrt(n)

D.

n

See Answer & Explanation Lets Discuss
Correct answer is : D
Explanation

=>E = (1/(21))*(21) + (1/(22))*(22) + … (1/(2n))*(2n)
= >1+1+…1 (n times addition of 1)=n
 

 
29

For each element in a set of size 2n, an unbiased coin is tossed. The 2n coin tosses are independent. An element is chosen if the corresponding coin toss were head. The probability that exactly n elements are chosen is:

A.

(2nCn) / (4^n

B.

(2nCn) / (2^n)

C.

1 / (2nCn)

D.

1/2

See Answer & Explanation Lets Discuss
Correct answer is : A
Explanation

Probability of n heads out of 2n coin tosses.
P = 2nCn∗((1/2)n)∗((1/2)n) = (2nCn) / (4n)

 
 

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