1
JEE Main 2022 (Online) 25th June Morning Shift
+4
-1 Let E1 and E2 be two events such that the conditional probabilities $$P({E_1}|{E_2}) = {1 \over 2}$$, $$P({E_2}|{E_1}) = {3 \over 4}$$ and $$P({E_1} \cap {E_2}) = {1 \over 8}$$. Then :

A
$$P({E_1} \cap {E_2}) = P({E_1})\,.\,P({E_2})$$
B
$$P(E{'_1} \cap E{'_2}) = P(E{'_1})\,.\,P(E{_2})$$
C
$$P({E_1} \cap E{'_2}) = P({E_1})\,.\,P({E_2})$$
D
$$P(E{'_1} \cap {E_2}) = P({E_1})\,.\,P({E_2})$$
2
JEE Main 2022 (Online) 24th June Evening Shift
+4
-1 A random variable X has the following probability distribution:

X 0 1 2 3 4
P(X) k 2k 4k 6k 8k

The value of P(1 < X < 4 | X $$\le$$ 2) is equal to :

A
$${4 \over 7}$$
B
$${2 \over 3}$$
C
$${3 \over 7}$$
D
$${4 \over 5}$$
3
JEE Main 2022 (Online) 24th June Morning Shift
+4
-1 Bag A contains 2 white, 1 black and 3 red balls and bag B contains 3 black, 2 red and n white balls. One bag is chosen at random and 2 balls drawn from it at random, are found to be 1 red and 1 black. If the probability that both balls come from Bag A is $${6 \over {11}}$$, then n is equal to __________.

A
13
B
6
C
4
D
3
4
JEE Main 2022 (Online) 24th June Morning Shift
+4
-1 If a random variable X follows the Binomial distribution B(33, p) such that

$$3P(X = 0) = P(X = 1)$$, then the value of $${{P(X = 15)} \over {P(X = 18)}} - {{P(X = 16)} \over {P(X = 17)}}$$ is equal to :

A
1320
B
1088
C
$${{120} \over {1331}}$$
D
$${{1088} \over {1089}}$$
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