(A) Let $E_A$ be the event that $A$ fails and $E_B$ be the event that $B$ fails.Given:$P(E_A) = 0.2$$P(E_A \cap E_B) = 0.15$The probability that $A$ f

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(A) Let $E_A$ be the event that $A$ fails and $E_B$ be the event that $B$ fails.Given:$P(E_A) = 0.2$$P(E_A \cap E_B) = 0.15$The probability that $A$ fails alone is given by the probability that $A$ fails minus the probability that both $A$ and $B$ fail.$P(A \text{ fails alone}) = P(E_A) - P(E_A \cap E_B)$Substituting the given values:$P(A \text{ fails alone}) = 0.2 - 0.15$$P(A \text{ fails alone}) = 0.05$

Class 11 Mathematics Set Theory Word Problem - Set Theory

Medium

An electronic assembly consists of two subsystems,$A$ and $B$. From previous testing procedures,the following probabilities are known:
$P(A \text{ fails}) = 0.2$
$P(B \text{ fails alone}) = 0.15$
$P(A \text{ and } B \text{ fail}) = 0.15$
Evaluate the probability $P(A \text{ fails alone})$.

A
$0.05$
B
$0.10$
C
$0.15$
D
$0.20$

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An electronic assembly consists of two subsystems,$A$ and $B$. From previous testing procedures,the following probabilities are known:$P(A \text{ fails}) = 0.2$$P(B \text{ fails alone}) = 0.15$$P(A \text{ and } B \text{ fail}) = 0.15$Evaluate the probability $P(A \text{ fails alone})$.

Similar Questions

In a class of $35$ students,$24$ like to play cricket and $16$ like to play football. Also,each student likes to play at least one of the two games. How many students like to play both cricket and football?

In a city,$20\%$ of persons read an English newspaper,$40\%$ read a Hindi newspaper,and $5\%$ read both newspapers. The percentage of people who do not read either paper is: (in $\%$)

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In a class of $55$ students,$23$ study Mathematics,$24$ study Physics,$19$ study Chemistry,$12$ study Mathematics and Physics,$9$ study Mathematics and Chemistry,$7$ study Physics and Chemistry,and $4$ study all three subjects. Find the number of students who study exactly one subject.

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An electronic assembly consists of two subsystems,$A$ and $B$. From previous testing procedures,the following probabilities are known:
$P(A \text{ fails}) = 0.2$
$P(B \text{ fails alone}) = 0.15$
$P(A \text{ and } B \text{ fail}) = 0.15$
Evaluate the probability $P(A \text{ fails alone})$.