GATE (CE) 2022: MATHEMATICS #6 (App update required to attempt this test)

If A and B are two independents events. If P(A) = 0.6 and P(A^CUB) = 0.6, then calculate the value of P(B).

Consider the following probability function of a random variable X such that

P(X) = 0.7 if X=0

0.3 if X= 1

0 other-wise.

Then calculate the variance of X.

Two dice each numbered from 1 to 6 are thrown together. Let A and B be two events given by

A: even number on the first dice.

B: number on the second dice is greater than 4

What is the value of P(AՈB) and P(AUB) respectively?

A point is randomly selected with uniform probability within the square in x-y plane bounded by x=0 to x=2 and y=0 to y=2. Find the expected value of L² where L is length of the line segment.

Two independent random variable X and Y are uniformly distributed in the interval of (-2, 2). The probability that max (X.Y) is less than 1 is

A die is tossed 180 times. If the probability of 6 turning up atleast 35 times is calculated through normal distribution, which of the following computations are correct for the above Data?

(Area under the normal b/w  and  is 0.35)
[Multiple Select Question]