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Two events A and B will be independent, then

A player participates in 3 matches against three teams T₁, T₂ and T₃.The probability of winning a match against teams T₁, T₂ and T₃ are 0.2, 0.3 and 0.9 respectively. If 'wins' can be regarded as independent events, then the probability that he

(A) wins all the 3 matches is 0.054

(B) wins no match is 0.054

(C) wins exactly two matches is 0.348

(D) wins exactly one match is 0.542

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If X is a random variable and a, b are real numbers, then which of the following statements are correct?

(A) $E[aX+b] = a E(X) + b$

(B) $Var (aX + b) = a^2 Var (X) + b$

(C) $Var (aX + b) = a Var (X)$

(D) $Var (X) = E(X^2) - [E(X)]^2$

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A die is tossed 6 times and getting "1 or 5" is considered a success. The probability of getting at least one success in six tosses is:

If the probability that an individual suffers a bad reaction from an injection of a given serum is 0.001. The probability that out of 2000 individuals, more than two individuals suffer from bad reaction is:

[Given that $e^{-2} \approx 0.13534$]

If a random variable $X$ has the following probability distribution:

, then

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Let x denote the number of doublets in three throws of a pair of dice with the following probability distribution.

If value of k is equal to $\frac{m}{n} \cdot \gcd(m,n) = 1$, then $m + n$ is equal to

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if $P(A) = \frac{3}{7}$, $P(B) = \frac{4}{7}$ and $P(A \cup B) = \frac{5}{7}$

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An urn contains 4 white and 3 red balls. In a random draw of three balls, the probability of

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If a computer code is correctly programmed, it gives 90% acceptable results. But if it is not correctly programmed, it gives only 40% acceptable results. From previous experience, it is observed that only 80% of codes are correctly programmed. If after a certain programming, the code gives 2 acceptable results, then the approximate probability that the code is correctly programmed is

If $2P(A) = P(B) = \frac{5}{13}$ and $P(A|B) = \frac{2}{5}$, then $P(A \cap B)$ is

Under which of the following conditions the Poisson distribution is the limiting case of, binomial distribution:

(A) The number of trials is indefinitely large.

(B) The probability of success for each trial is indefinitely small.

(C) The product of the number of trials and the probability of success for each trial is finite.

(D) The probability of success for each trial is indefinitely large.

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If $X$ is a normal variate with mean 12 and standard deviation 4, then $P[X \ge 20]$ is:

[Given that: $P[0 \le Z \le 2] = 0.4772]$

In a game, a man wins Rs. 5 for getting a number greater than 4 and loses Rs. 1 otherwise, when a fair dice is thrown. The man decided to throw a die thrice but to quit as and when he gets a number greater than 4. The expected value of the amount(in Rs.) he wins or loses is:

The probability of a man hitting a target is 1/2. How many times must he fire so that the probability of hitting the target at least once is more than 90%?

Let the random variable X represent the positive difference between the number of heads and the number of tails obtained when a coin is tossed 6 times. Then probability $P(X \leq 3)$ is equal to

An urn I contains 3 white and 4 blue balls, while urn II contains 5 white and 6 blue balls. One ball is drawn at random from one of the urns and it is found to be white. The probability that it was drawn from urn II is

If a person A speaks the truth in 80% cases and the person B speaks the truth in 75% cases, then the probability that they contradict each other in a statement is

A problem in Mathematics is given to two students X and Y whose chances of solving it are $\frac{1}{3}$ and $\frac{1}{4}$ respectively. The probability that only X solves the problem, is:

If we take 8 identical slips of paper and write the number 0 on one of them, the number 1 on three of the slips, the number 2 on three of the slips and the number 3 on one of the slips. These slips are folded, put in a box and roughly mixed. One slip is drawn at random from the box. If X is the random variable denoting the number written on the drawn slip, the variance of X is:

The normal distribution curve is symmetrical about

[$\mu$ = mean, $\sigma$= standard deviation]

In a game, a person is paid Rs. 2 if he gets all heads or all tails when three coins are tossed, and he will pay Rs. 2 if either one or two heads show. What can he expect to win on an average per game?

A lot of 50 watches is known to have 10 defective watches. If 8 watches are selected one by one with a replacement at random, then the probability that there will be at least one defective watch is:

The probability distribution of a random variable X is given by

If $a > 0$, then $P(0 < x \leq 2)$ is equal to

A black and a red die are rolled simultaneously. The probability of obtaining a sum greater than 9, given that the black resulted in a 5 is

If A and B are any two events such that P(B) = P(A and B), then which of the following is correct

If A is any event associated with sample space and If $E_1, E_2, E_3$ are mutually exclusive and exhaustive events. Then which of the following are true?

(A) $P(A) = P(E_1)P(E_2|A) + P(E_2)P(E_2|A) + P(E_3)P(E_3|A)$

(B) $P(A) = P(A|E_1)P(E_1) + P(A|E_2)P(E_2) + P(A|E_3)P(E_3)$

(C) $P(E_i|A) = \frac{P(A|E_i)P(E_i)}{\sum_{i=1}^3 P(A|E_i)P(E_i)}$, $i = 1,2,3$

(D) $P(A|E_i) = \frac{P(E_i|A)P(E_i)}{\sum_{i=1}^3 P(E_i|A)P(E_i)}$, $i = 1,2,3$

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Let A & B are two events such that P(A)=0.8, P(B)=0.5, P(B|A)=0.4

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What is the mean of the numbers obtained on throwing a die having written 1 on three faces, 2 on two faces and 5 on 1 face?

How many minimum number of times must a man toss a fair coin so that the probability of having at least one head is more than 90%?