1
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
$$\frac{3}{4}$$
2
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
$$P(A) = {2 \over 3},P(B) = {1 \over 8}$$
3
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
$$\mathrm{p_1 < p_{16} < p_5}$$
4
WB JEE 2022
+1
-0.25

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
[0, 1]
B
$$\left[ {{1 \over 3},{1 \over 2}} \right]$$
C
$$\left[ {{1 \over 3},{2 \over 3}} \right]$$
D
$$\left[ {{1 \over 3},{{13} \over 3}} \right]$$
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