(B) Let $P(A) = 0.6$, $P(B) = 0.5$, $P(C) = 0.4$.Given intersections: $P(A \cap B) = 0.3$, $P(B \cap C) = 0.2$, $P(A \cap C) = 0.2$, $P(A \cap B \cap

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(B) Let $P(A) = 0.6$, $P(B) = 0.5$, $P(C) = 0.4$.Given intersections: $P(A \cap B) = 0.3$, $P(B \cap C) = 0.2$, $P(A \cap C) = 0.2$, $P(A \cap B \cap C) = 0.1$.The probability of succeeding in exactly one test is given by: $P(\text{exactly one}) = P(A) + P(B) + P(C) - 2[P(A \cap B) + P(B \cap C) + P(A \cap C)] + 3P(A \cap B \cap C)$.Substituting the values: $P(\text{exactly one}) = 0.6 + 0.5 + 0.4 - 2[0.3 + 0.2 + 0.2] + 3[0.1]$.$P(\text{exactly one}) = 1.5 - 2[0.7] + 0.3$.$P(\text{exactly one}) = 1.5 - 1.4 + 0.3 = 0.4$.

Class 11 Mathematics Set Theory Word Problem - Set Theory

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If the probabilities of a student succeeding in the entrance tests for institutes $A$, $B$ and $C$ are $0.6$, $0.5$ and $0.4$ respectively, while the probability of succeeding in both $A$ and $B$ is $0.3$, in both $B$ and $C$ is $0.2$, in both $A$ and $C$ is $0.2$, and in all three is $0.1$, then the probability that the student succeeds in exactly one of these tests is......

MHT CET 2026 All MHT CET

A
$0.3$
B
$0.4$
C
$0.5$
D
$0.6$

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There are exactly twelve Sundays in the period from January $1$ to March $31$ in a certain year. Then,the day corresponding to February $15$ in that year is

KVPY 2017

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$X, Y, Z$ are the sets of all positive divisors of $10^{60}, 20^{50},$ and $30^{40}$ respectively. Find $n(X \cup Y \cup Z)$.

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In a class of $60$ students,$30$ opted for $NCC$,$32$ opted for $NSS$,and $24$ opted for both $NCC$ and $NSS$. If one of these students is selected at random,find the probability that the student opted for $NCC$ or $NSS$.

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If $n(X)=700, n(A)=200, n(B)=300,$ and $n(A \cap B)=100$,where $X$ is the universal set and $A$ and $B$ are subsets of $X$,then $n(A' \cap B')=$

MediumMHT CET 2020

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In a certain town,$25\%$ of the families own a phone and $15\%$ own a car; $65\%$ families own neither a phone nor a car and $2,000$ families own both a car and a phone. Consider the following three statements:
$(A) \, 5\%$ families own both a car and a phone
$(B) \, 35\%$ families own either a car or a phone
$(C) \, 40,000$ families live in the town
Then,

DifficultJEE MAIN 2015

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There are exactly twelve Sundays in the period from January $1$ to March $31$ in a certain year. Then,the day corresponding to February $15$ in that year is

$X, Y, Z$ are the sets of all positive divisors of $10^{60}, 20^{50},$ and $30^{40}$ respectively. Find $n(X \cup Y \cup Z)$.

In a class of $60$ students,$30$ opted for $NCC$,$32$ opted for $NSS$,and $24$ opted for both $NCC$ and $NSS$. If one of these students is selected at random,find the probability that the student opted for $NCC$ or $NSS$.

If $n(X)=700, n(A)=200, n(B)=300,$ and $n(A \cap B)=100$,where $X$ is the universal set and $A$ and $B$ are subsets of $X$,then $n(A' \cap B')=$

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