Three students A, B, and C are given a mathem | vedclass

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Question

(A) Let $P(A), P(B),$ and $P(C)$ be the probabilities of students $A, B,$ and $C$ solving the problem respectively.$P(A) = 1/2, P(B) = 1/3, P(C) = 1/4

Vedclass · Accepted Answer

$3/4$

Vedclass · Answer

(A) Let $P(A), P(B),$ and $P(C)$ be the probabilities of students $A, B,$ and $C$ solving the problem respectively.$P(A) = 1/2, P(B) = 1/3, P(C) = 1/4$.The probability that the problem is not solved by any of them is the probability that all three fail to solve it.$P(	ext{not } A) = 1 - 1/2 = 1/2$$P(	ext{not } B) = 1 - 1/3 = 2/3$$P(	ext{not } C) = 1 - 1/4 = 3/4$Since the events are independent,the probability that none of them solve the problem is:$P(	ext{none solve}) = P(	ext{not } A) 	imes P(	ext{not } B) 	imes P(	ext{not } C) = \frac{1}{2} 	imes \frac{2}{3} 	imes \frac{3}{4} = \frac{1}{4}$.The probability that the problem is solved is $1 - P(	ext{none solve})$.$P(	ext{solved}) = 1 - \frac{1}{4} = \frac{3}{4}$.

List $I$	List $II$
$(i) \ P(A \cap B)$	$(1) \ 0.4$
$(ii) \ P(A \cap \bar{B})$	$(2) \ 0.2$
$(iii) \ P(\bar{A} \cap B)$	$(3) \ 0.3$
$(iv) \ P(\bar{A} \cap \bar{B})$	$(4) \ 0.1$

List-$I$	List-$II$
$(i) \ P(A \cap B)$	$(1) \ 0.4$
$(ii) \ P(A \cap \bar{B})$	$(2) \ 0.2$
$(iii) \ P(\bar{A} \cap B)$	$(3) \ 0.3$
$(iv) \ P(\bar{A} \cap \bar{B})$	$(4) \ 0.1$

Three students $A, B,$ and $C$ are given a mathematics problem. The probabilities of them solving the problem are $1/2, 1/3,$ and $1/4$ respectively. What is the probability that the problem is solved?

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