the probability of solving a question by ABC is 1/2, 1/3, 1/4 respectively find the probability 1) exactly one of them will solve the question 2) exactly two of them solve the question 3) question is not solved 4) at least one of them solve the question please show the process
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Answered by
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Step-by-step explanation:
Probability exactly one of A,B or C solves it
= probability of A solving (remaining fail) + probability of B solving (remaining fail) + probability of C solves (remaining fail)
=P(A)×P(B
C
)×P(C
C
)+P(A
C
)P(B)P(C
C
)+P(A
C
)P(B
C
)P(C)
=(
3
1
)(1−
7
2
)(1−
8
3
)+(1−
3
1
)(
7
2
)(1−
8
3
)+(1−
3
1
)(1−
7
2
)(
8
3
)
=
3
1
×
7
5
×
8
5
+
3
2
×
7
2
×
8
5
+
3
2
×
7
5
×
8
3
⇒
168
25
+
168
20
+
168
30
⇒
168
75
⇒
56
25
probability that exactly one will solve is
56
25
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