Probability - Algebra - Mathematics PYQ

P speaks truth in 70% of the cases and Q in 80% of the cases. In what percent of cases are they likely to agree in stating the same fact

A coin is tossed 2020 times. The probability of getting head on 1947th toss is

If \(A\) and \(B\) are two events with \(P(A \cap B)=\frac{1}{3}, P(A \cup B)=\frac{5}{6}\) and \(P\left(A^C\right)=\frac{1}{2}\), then the value of \(P\left(B^C\right)\) is

A discrete random variable X takes values 10, 20, 30 and 40. with probability 0.3, 0.3, 0.2 and 0.2 respectively. Then the expected value of X is

Let \(X\) be a random variable which takes values \(1,2,3,4\) such that \(P(X=r)=K r^3\) where \(r=1,2,3,4\) then

A random variable X has the probability distribution

For the events E = {X is a prime number} and F = {X < 4}, then P(E \(\cup\) F) is

12 balls are distributed among 3 boxes, then the probability that the first box will contain 3 balls is

A die is tossed thrice. If event of getting an even number is a success, then the probability of getting at least 2 successes is

A coin is tossed until a head appears or it has been tossed thrice. Given that head doesn’t appear on the first toss, the probability that coin tossed thrice is

Tom and Jerry play a game of alternately throwing an unfair coin. First one to get head wins. If Tom starts the game, he has 62.5% chance of winning the game. Suppose this coin is tossed 5 times, then the probability of getting exactly 3 head is

Box-I contains 3 cards bearing numbers 1, 2, 3 , Box II contains 5 cards bearing numbers 1 , 2, 3, 4, 5 and Box III contains 7 cards bearing numbers 1, 2, 3, 4, 5, 6, 7. One card is drawn at random from each of the boxes. If \(x_i\) be the number on the card drawn from the \(i\) th box, \(i=1,2,3\), then the probability that \(x_1+x_2+x_3\) is odd is equal to

The range of a random variable \(X\) is \(\{1,2,3, \ldots\}\) and \(P(X=x)=\frac{C^x}{x !}\). for \(x=1,2,3\), ... Then, the value of \(C\) is

Nine balls one drawn simultaneously from a bag containing 5 white and 7 black balls. The probability of drawing 3 white and 6 black balls is

The probabilities that \(A\) and \(B\) speak truth are \(\frac{4}{5}\) and \(\frac{3}{4}\) respectively. The probability that they contradict each other when asked to speak on a fact is

One card is selected at random from 27 cards numbered form 1 to 27. What is the probability that the number on the card is even or divisible by 5.

The mean and variance of a binomial variable X are 2 and 1 respectively. The probability that X takes values greater than 1 is

In a box, there are 8 red, 7 blue and 6 green balls. One ball is picked randomly. The probability that it is neither red nor green is

Which of the following is not a property of a Binomial distribution?

Five digit numbers are formed by using digits \(1,2,3,4\) and 5 without repetition. Then, the probability that the randomly chosen number is divisible by 4 is

A manager decides to distribute ₹ 20000 between two employees \(X\) and \(Y\). He knows \(X\) deserves more than \(Y\), but does not know how much more. So, he decides to arbitrarily break ₹ 20000 into two parts and give \(X\) the bigger part. Then, the chance that \(X\) gets twice as much as \(Y\) or more is