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

Consider the sequence of numbers $(1,2,3, \ldots \ldots, 13)$. A person choose three numbers at random from the sequence. The probability that the chosen three number form an A.P. is

A mapping is selected at random from all mappings $f: A \rightarrow A$, where set $A=\{1,2,3 \ldots, n\}$. If the probability that the mapping is injective is $\frac{3}{32}$, then the value of $n$ is

If ' $a$ ' is an integer lying in $[-5,30]$, then the probability that the graph of $y=x^2+2(a+4) x-5 a+64$ lies above the $x-$ axis is

Four natural numbers selected at random are multiplied together, then the probability that the digit in the unit's place in the product be $1,3,7$ or 9 is

If $E$ and $F$ are two independent events with $P(E)=0.3$ and $P(E \cup F)=0.5$, then $P(E / F)-P(F / E)$ equals

The probability that a non-leap year selected at random will have 53 Sundays or 53 Saturdays is

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 $$\mathrm{P}(\mathrm{r} \leq \mathrm{k} / \mathrm{s} \leq \mathrm{k})=$$

(k is an integer < n)

A biased coin with probability $$\mathrm{p}(0<\mathrm{p}<1)$$ of getting head is tossed until a head appears for the first time. If the probability that the number of tosses required is even is $$\frac{2}{5}$$, then $$\mathrm{p}=$$

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 $${1 \over 2}$$. Then

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 $$\mathrm{p_k=P(E_k)}$$, then the correct among the following is :

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 the set of possible values of x are in

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 is non-zero is

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

If $A_1, A_2, A_3, \ldots, A_{1006}$ be independent events such that $P\left(A_l\right)=\frac{1}{2 i},(i=1,2, \ldots, 1006)$ and the probability that none of the events occurs be $\frac{\alpha!}{2^a(\beta!)^2}$ ，then

Three numbers are chosen at random without replacement from $\{1,2, \ldots 10\}$. The probability that the minimum of the chosen numbers is 3 or their maximum is 7 , is