SATHEE: Probability 2 Question 9

Probability 2 Question 9

9. If $M$ and $N$ are any two events, then the probability that exactly one of them occurs is

(a) $P (M) + P (N) - 2 P (M \cap N)$

(1984, 3M)

(b) $P (M) + P (N) - P (\overset{―}{M \cup N})$

(d) $P (M \cap \bar{N}) - P (\bar{M} \cap N)$

Fill in the Blanks

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Answer:

Correct Answer: 9. $(a, b, c)$

Solution:

$P$ (exactly one of $M, N$ occurs)

$= P (M \cap \bar{N}) \cup (\bar{M} \cap N) = P (M \cap \bar{N}) + P (\bar{M} \cap N)$

$= P (M) - P (M \cap N) + P (N) - P (M \cap N)$

$= P (M) + P (N) - 2 P (M \cap N)$

Also, $P$ (exactly one of them occurs)

$= 1 - P (\bar{M} \cap \bar{N}) 1 - P (\bar{M} \cup \bar{N})$

$= P (\bar{M} \cup \bar{N}) - P (\bar{M} \cap \bar{N}) = P (\bar{M}) + P (\bar{N}) - 2 P (\bar{M} \cap \bar{N})$

Hence, (a) and (c) are correct answers.

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Probability 2 Question 9

9. If M and N are any two events, then the probability that exactly one of them occurs is

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9. If $M$ and $N$ are any two events, then the probability that exactly one of them occurs is