1
WB JEE 2024
+1
-0.25

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
$$\frac{\mathrm{k}}{\mathrm{n}}$$
B
$$\frac{\mathrm{k}}{\mathrm{n}-1}$$
C
$$\frac{\mathrm{k}-1}{\mathrm{n}}$$
D
$$\frac{k-1}{n-1}$$
2
WB JEE 2024
+1
-0.25

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 $$\mathrm{p}=$$

A
$$\frac{1}{4}$$
B
$$\frac{1}{3}$$
C
$$\frac{2}{3}$$
D
$$\frac{3}{4}$$
3
WB JEE 2023
+1
-0.25

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

A
$$P(A) = {1 \over 3},P(B) = {1 \over 4}$$
B
$$P(A) = {1 \over 2},P(B) = {1 \over 6}$$
C
$$P(A) = {1 \over 6},P(B) = {1 \over 2}$$
D
$$P(A) = {2 \over 3},P(B) = {1 \over 8}$$
4
WB JEE 2023
+1
-0.25

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
$$\mathrm{p_1 < p_{10} < p_4}$$
B
$$\mathrm{p_1 < p_{8} < p_{14}}$$
C
$$\mathrm{p_1 < p_{8} < p_{17}}$$
D
$$\mathrm{p_1 < p_{16} < p_5}$$
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