Probability that a student will succeed in IIT entrance test is 0.2 and that he will succeed in Roor

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14.Probability

hard

Probability that a student will succeed in $IIT$ entrance test is $0.2$ and that he will succeed in Roorkee entrance test is $0.5$. If the probability that he will be successful at both the places is $0.3$, then the probability that he does not succeed at both the places is

$0.4$

$0.3$

$0.2$

$0.6$

Solution

(d) Let $A$ denotes the event that the student is selected in $IIT$ entrance test and $B$ denotes the event that he is selected in Roorkee entrance test. Then

$P(A) = 0.2,\,\,P(B) = 0.5$ and $P(A \cap B) = 0.3.$

Required probability $ = P(\overline A \cap \overline B) = 1 – P(A \cup B)$

$ = 1 – (P(A) + P(B) – P(A \cap B))$

$ = 1 – (0.2 + 0.5 – 0.3) = 0.6$.

Standard 11

Mathematics

Two students Anil and Ashima appeared in an examination. The probability that Anil will qualify the examination is $0.05$ and that Ashima will qualify the examination is $0.10 .$ The probability that both will qualify the examination is $0.02 .$ Find the probability that Both Anil and Ashima will not qualify the examination.

medium

Two balls are drawn at random with replacement from a box containing $10$ black and $8$ red balls. Find the probability that First ball is black and second is red.

easy

A card is drawn from a pack of $52$ cards. A gambler bets that it is a spade or an ace. What are the odds against his winning this bet

easy

If odds against solving a question by three students are $2 : 1 , 5:2$ and $5:3$ respectively, then probability that the question is solved only by one student is

medium

$A$ and $B$ are events such that $P(A)=0.42$, $P(B)=0.48$ and $P(A$ and $B)=0.16 .$ Determine $P ($ not $A ).$

easy

Probability that a student will succeed in $IIT$ entrance test is $0.2$ and that he will succeed in Roorkee entrance test is $0.5$. If the probability that he will be successful at both the places is $0.3$, then the probability that he does not succeed at both the places is

Solution

Similar Questions

Two balls are drawn at random with replacement from a box containing $10$ black and $8$ red balls. Find the probability that First ball is black and second is red.

A card is drawn from a pack of $52$ cards. A gambler bets that it is a spade or an ace. What are the odds against his winning this bet

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