# The probabilities that a student will solve Question A and Question B are $0.4$ and $0.5$ respectively. What is the probability that he solves at least one of the two questions?

A.$0.6$

B.$0.7$

C.$0.8$

D.$0.9$

Answer

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Hint : Consider an event which is not happening.

Given probabilities that a student will solve Question A and Question B are $0.4$ and $0.5$ respectively

Probability the student will not solve either question A or B are \[1 - 0.4 = 0.6\;\]and \[1 - 0.5 = 0.5\;\,\]respectively

And

Total probability the student will not solve any question is $0.6 \times 0.5 = 0.3$

Probability that he solves at least one of the two questions,

=(total probability) - (probability the student will not solve any question)=\[\;1 - \left( {0.6 \times 0.5} \right) = 1 - 0.3 = 0.7\]

Therefore, Correct answer is option B.

Note :- In these types of questions of probability we have to obtain the probability of not happening of an event then subtract with the total probability (which is 1 ) to get the probability of happening of that event.

Given probabilities that a student will solve Question A and Question B are $0.4$ and $0.5$ respectively

Probability the student will not solve either question A or B are \[1 - 0.4 = 0.6\;\]and \[1 - 0.5 = 0.5\;\,\]respectively

And

Total probability the student will not solve any question is $0.6 \times 0.5 = 0.3$

Probability that he solves at least one of the two questions,

=(total probability) - (probability the student will not solve any question)=\[\;1 - \left( {0.6 \times 0.5} \right) = 1 - 0.3 = 0.7\]

Therefore, Correct answer is option B.

Note :- In these types of questions of probability we have to obtain the probability of not happening of an event then subtract with the total probability (which is 1 ) to get the probability of happening of that event.

Last updated date: 28th Sep 2023

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