1
JEE Main 2022 (Online) 26th June Morning Shift
+4
-1
Out of Syllabus

Let a biased coin be tossed 5 times. If the probability of getting 4 heads is equal to the probability of getting 5 heads, then the probability of getting atmost two heads is :

A
$${{275} \over {{6^5}}}$$
B
$${{36} \over {{5^4}}}$$
C
$${{181} \over {{5^5}}}$$
D
$${{46} \over {{6^4}}}$$
2
JEE Main 2022 (Online) 25th June Evening Shift
+4
-1

A biased die is marked with numbers 2, 4, 8, 16, 32, 32 on its faces and the probability of getting a face with mark n is $${1 \over n}$$. If the die is thrown thrice, then the probability, that the sum of the numbers obtained is 48, is :

A
$${7 \over {{2^{11}}}}$$
B
$${7 \over {{2^{12}}}}$$
C
$${3 \over {{2^{10}}}}$$
D
$${{13} \over {{2^{12}}}}$$
3
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
$$P(E{'_1} \cap {E_2}) = P({E_1})\,.\,P({E_2})$$
4
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
$${4 \over 5}$$
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