Algebra

Probability

Medium

core

The probabilities of occurrance of two events A and B are 0.45 and 0.20 respectively. The probability of their simultaneous occurrence is 0.06. The probability that neither A nor B occurs is

0.41

0.59

✅ Correct Option: 3

Given:

$P(A) = 0.45$

$P(B) = 0.20$

$P(A \cap B) = 0.06$

The probability that neither A nor B occurs is the complement of the probability that at least one of them occurs.

Using the addition rule of probability:

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

$P(A \cup B) = 0.45 + 0.20 - 0.06$

$P(A \cup B) = 0.65 - 0.06$

$P(A \cup B) = 0.59$

The probability that neither A nor B occurs:

$P(\text{neither A nor B}) = 1 - P(A \cup B)$

$P(\text{neither A nor B}) = 1 - 0.59$

$P(\text{neither A nor B}) = 0.41$

Therefore, the probability that neither A nor B occurs is $0.41$ .

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Match the LIST-I with LIST-II

LIST-I	LIST-II
A. $P(A \cap B) + P(A \cap \overline{B})$	I. $P(A \cup B)$
B. $P(A \cap B) + P(\overline{A} \cap B)$	II. $P(A) + P(B)$
C. $P(A \cap B) + P(\overline{A} \cap B) + P(A \cap \overline{B})$	III. $P(A)$
D. $P(A \cup B) + P(A \cap B)$	IV. $P(B)$

Choose the correct answer from the options given below:

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Consider an experiment of tossing 3 coins simultaneously. Define the following events:

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Choose the correct option:

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Solution

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