Probability · Mathematics · WB JEE
MCQ (Single Correct Answer)
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
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
Subjective
MCQ (More than One Correct Answer)
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