Probability · Mathematics · WB JEE

A person draws out two balls successively from a bag containing 6 red and 4 white balls. The probability that at least one of them will be red is...

A and B are two independent events such that P(A $$\cup$$ B') = 0.8 and P(A) = 0.3. Then P(B) is

Three numbers are chosen at random from 1 to 20. The probability that they are consecutive is

Two dice are tossed once. The probability of getting an even number at the first die or a a total of 8 is

The probability that at least one of A and B occurs is 0.6. If A and B occur simultaneously with probability 0.3, then P(A') + P(B') is

4 boys and 2 girls occupy seats in a row at random. Then the probability that the two girls occupy seats side by side is

A coin is tossed again and again. If tail appears on first three tosses, then the chance that head appears on fourth toss is

Two decks of playing cards are well shuffled and 26 cards are randomly distributed to a player. Then, the probability that the player gets all distinc...

Two smallest squares are chosen one by one on a chess board. The probability that they have a side in common is

Two integers $$\mathrm{r}$$ and $$\mathrm{s}$$ are drawn one at a time without replacement from the set $$\{1,2, \ldots, \mathrm{n}\}$$. Then $$\mathr...

A biased coin with probability $$\mathrm{p}(0...

Let A and B are two independent events. The probability that both A and B happen is $${1 \over {12}}$$ and probability that neither A and B happen is ...

Let S be the sample space of the random experiment of throwing simultaneously two unbiased dice and $$\mathrm{E_k=\{(a,b)\in S:ab=k\}}$$. If $$\mathrm...

A, B, C are mutually exclusive events such that $$P(A) = {{3x + 1} \over 3}$$, $$P(B) = {{1 - x} \over 4}$$ and $$P(C) = {{1 - 2x} \over 2}$$. Then th...

A determinant is chosen at random from the set of all determinants of order 2 with elements 0 or 1 only. The probability that the determinant chosen i...

Four persons A, B, C and D throw and unbiased die, turn by turn, in succession till one gets an even number and win the game. What is the probability ...

Four persons A, B, C and D throw an unbiased die, turn by turn, in succession till one gets an even number and win the game. What is the probability t...

A rifleman is firing at a distant target and has only 10% chance of hitting it. The least number of rounds he must fire to have more than 50% chance o...

A problem in mathematics is given to 4 students whose chances of solving individually are $${{1 \over 2}}$$, $${{1 \over 3}}$$, $${{1 \over 4}}$$ and ...

If X is a random variable such that $$\sigma$$(X) = 2.6, then $$\sigma$$(1 $$-$$ 4X) is equal to

In order to get a head at least once with probability $$ \ge $$ 0.9, the minimum number of times a unbiased coin needs to be tossed is

A student appears for tests I, II and III. The student is successful if he passes in tests I, II or I, III. The probabilities of the student passing i...

The probability that a non-leap year selected at random will have 53 Sunday is

If an unbiased coin is tossed n times. Find the probability that head appears an odd number of times.

A and B are independent events. The probability that both A and B occur is $${1 \over {20}}$$ and the probability that neither of them occurs is $${3 ...