JEE MAIN - Mathematics (2020 - 8th January Evening Slot - No. 8)
Let A and B be two events such that the
probability that exactly one of them occurs is $${2 \over 5}$$ and the probability that A or B occurs is $${1 \over 2}$$ ,
then the probability of both of them occur
together is :
0.20
0.02
0.01
0.10
Explanation
Probability that exactly one of them occurs
P(A) + P(B) – 2P (A $$ \cap $$ B) = $${2 \over 5}$$ .....(1)
Probability that A or B occurs is
P(A) + P(B) – P(A $$ \cap $$ B) = $${1 \over 2}$$ ......(2)
Doing (2) - (1)
P(A $$ \cap $$ B) = $${1 \over 2} - {2 \over 5}$$ = 0.10
P(A) + P(B) – 2P (A $$ \cap $$ B) = $${2 \over 5}$$ .....(1)
Probability that A or B occurs is
P(A) + P(B) – P(A $$ \cap $$ B) = $${1 \over 2}$$ ......(2)
Doing (2) - (1)
P(A $$ \cap $$ B) = $${1 \over 2} - {2 \over 5}$$ = 0.10
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