Probability - Online Test
Q1. Find the mean number of heads in three tosses of a fair coin.
Answer : Option C
Explaination / Solution:
Let X is the random variable of “number of heads “ X = 0, 1, 2, 3.
Therefore, the probability distribution is:
Therefore, the probability distribution is:
Q2. Two dice are thrown simultaneously. If X denotes the number of sixes, find the expectation of X.
Answer : Option B
Explaination / Solution:
Let A = event of getting 6 on the dice .
A = {(6,1),(6,2),(6,3),(6,4),(6,5),(6,6),(1,6),(2,6),(3,6),(4,6),(5,6)}
Let X is the random variable of “ number of sixes “.
Therefore, X = 0 , 1, ,2 .
A = {(6,1),(6,2),(6,3),(6,4),(6,5),(6,6),(1,6),(2,6),(3,6),(4,6),(5,6)}
Let X is the random variable of “ number of sixes “.
Therefore, X = 0 , 1, ,2 .
Q3. Two numbers are selected at random (without replacement) from the first six positive integers. Let X denote the larger of the two numbers obtained. Find E(X).
Answer : Option B
Explaination / Solution:
First 6 positive integers are 1,2,3,4,5,6. As 1 is the smallest positive integer. Therefore , X = 2,3,4,5,6.
Q4. In a meeting, 70% of the members favour and 30% oppose a certain proposal.A member is selected at random and we take X = 0 if he opposed, and X = 1 if he is in favour. Find E(X) and Var (X).
Answer : Option C
Explaination / Solution:
Here X = 0, 1.
Therefore, the probability distribution is:
Therefore, the probability distribution is:
