List of top Data Science and Artificial Intelligence Questions on Probability asked in GATE AR

A fair six-sided die (with faces numbered 1, 2, 3, 4, 5, 6) is repeatedly thrown independently.
What is the expected number of times the die is thrown until two consecutive throws of even numbers are seen ?

Consider a joint probability density function of two random variables X and Y
\(f_{x,y}(x,y) = \left\{ \begin{array}{ll} 2xy, & 0\lt x \lt2 , & 0\lt y\lt x\\ 0 & \text{otherwise } \end{array} \right.\)
Then, E[Y | X = 1.5] is ______.

Let game(ball, rugby) be true if the ball is used in rugby and false otherwise.
Let shape(ball, round) be true if the ball is round and false otherwise.
Consider the following logical sentences :
s1: ∀ball ¬ game(ball, rugby) ⇒shape(ball, round)
s2: ∀ball ¬ shape(ball, round) ⇒game(ball, rugby)
s3: ∀ball game(ball, rugby) ⇒ ¬shape(ball, round)
s4: ∀ball shape(ball, round) ⇒ ¬ game(ball, rugby)
Which of the following choices is/are logical representations of the assertion,
“All balls are round except balls used in rugby”?

Consider two events T and S. Let \(\bar{T}\) denote the complement of the event T. The probability associated with different events are given as follows :
 P(\(\bar{T}\)) = 0.6, P(S|T) = 0.3, P(SI\(\bar{T}\)) = 0.6
Then, P(TIS) is ______
(rounded off to two decimal places)

The sample average of 50 data points is 40. The updated sample average after including a new data point taking the value of 142 is _____.

Let the minimum, maximum, mean and standard deviation values for the attribute income of data scientists be ₹46000, ₹170000, ₹96000, and ₹21000, respectively. The z-score normalized income value of 106000 is closest to which ONE of the following options ?

Consider the following statements :
(i) The mean and variance of a Poisson random variable are equal.
(ii) For a standard normal random variable, the mean is zero and the variance is one.
Which ONE of the following options is correct ?

Three fair coins are tossed independently. T is the event that two or more tosses result in heads. S is the event that two or more tosses result in tails. What is the probability of the event T ∩ S?

When 3 coins are tossed,what is the prob of getting 2 heads 1 tail intersection 2 tails one head?

Find P(TIS) if P(T') = 0.6 P(SIT)=0.3 P(S(T')=0.3

A die is thrown repeatedly. Expected number of throws required until two consecutive throws shows an even number____.

Find P(\(\frac{T}{S}\)) If P(T')=0.6P(SIT)=0.3 P (S(T'))=0.3

If the probability of having boy or girl 0.3, what is probability of getting 2 girls 1 boy?