Question

If A and B are mutually exclusive and P(A)=0.29,P(B)=0.43. Find
a) , b) P , c) P

Answer 1

Answer on Question #45531, Engineering, SolidWorks

Problem.

If A and B are mutually exclusive and $P(A) = 0.29, P(B) = 0.43$. Find

a) , b) P , c) P

Remark.

The part of the question is missed. I suppose that this is question from Super Course in Mathematics for the IIT-JEE: Algebra II. The full statement is:

"If $A$ and $B$ are mutually exclusive and $P(A) = 0.29, P(B) = 0.43$. Find

a) $P(A')$, b) $P(A \cup B)$, c) $P(A \cap B')$, d) $P(A' \cap B')$.

Solution.

Since $A$ and $B$ are mutually exclusive events $A \cap B = \emptyset$ and $P(A \cap B) = 0$.

a) $P(A') = 1 - P(A) = 0.71$;

b) $P(A \cup B) = P(A) + P(B) - P(A \cap B) = P(A) + P(B) = 0.72$.

c) $P(A \cap B') = P(A) = 0.29$, as $A$ is a subset of $B'$ ($A$ and $B$ are mutually exclusive).

d) $P(A' \cap B') = P((A \cup B)' = 1 - P(A \cup B) = 0.28$, by De Morgan's law.

Answer: a) $P(A') = 0.71$; b) $P(A \cup B) = 0.72$; c) $P(A \cap B') = 0.29$; d) $P(A' \cap B') = 0.28$.

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