(D) Given data:$P(A \text{ fails}) = 0.2$$P(A \cap B \text{ fail}) = 0.15$To find the probability that $A$ fails alone, we subtract the probability th

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(D) Given data:$P(A \text{ fails}) = 0.2$$P(A \cap B \text{ fail}) = 0.15$To find the probability that $A$ fails alone, we subtract the probability that both $A$ and $B$ fail from the total probability that $A$ fails.$P(A \text{ fails alone}) = P(A \text{ fails}) - P(A \cap B \text{ fail})$$P(A \text{ fails alone}) = 0.2 - 0.15 = 0.05$Thus, the correct option is $D$.

Class 11 Mathematics Set Theory Word Problem - Set Theory

Easy

An electronic assembly consists of two subsystems $A$ and $B$. Past testing procedures data show that probabilities of failure are $P(A \text{ fails}) = 0.2$, $P(B \text{ fails alone}) = 0.15$, and $P(A \cap B \text{ fail}) = 0.15$. Then the probability that $A$ fails alone is equal to

AP EAMCET 2020 All AP EAMCET

A
$0.02$
B
$0.03$
C
$0.04$
D
$0.05$

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Set Theory

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Word Problem - Set Theory

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DifficultKVPY 2017

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An electronic assembly consists of two subsystems $A$ and $B$. Past testing procedures data show that probabilities of failure are $P(A \text{ fails}) = 0.2$, $P(B \text{ fails alone}) = 0.15$, and $P(A \cap B \text{ fail}) = 0.15$. Then the probability that $A$ fails alone is equal to

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In a classroom,one-fifth of the boys leave the class and the ratio of the remaining boys to girls is $2:3$. If further $44$ girls leave the class,the ratio of boys to girls becomes $5:2$. How many more boys should leave the class so that the number of boys equals that of girls?

In a committee,$50$ people speak French,$20$ speak Spanish and $10$ speak both Spanish and French. How many speak at least one of these two languages?

Out of $500$ car owners investigated,$400$ owned car $A$ and $200$ owned car $B$,and $50$ owned both car $A$ and car $B$. Is this data correct?

In a class of $125$ students,$70$ passed in Mathematics,$55$ in Statistics,and $30$ in both. The probability that a student selected at random from the class has passed in only one subject is

If $X$ and $Y$ are two sets such that $X \cup Y$ has $50$ elements,$X$ has $28$ elements and $Y$ has $32$ elements,how many elements does $X \cap Y$ have?

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