For any two events A and B, the probability that at least one of them

1.	For any two events A and B, the probability that at least one of them occur is 0.6. If A and B occur simultaneously with a probability 0.3, then P(A') + P(B') is 1. 0.92. 1.153. 1.14. 1.0
Answer» Correct Answer - Option 3 : 1.1 Concept: we know that, \(\rm P(A) +P(B) = P(A \cup B) + P(A \cap B)\) P(A') = 1 - P(A) Calculations: Given, For any two events A and B, the probability that at least one of them occur is 0.6 ⇒ \(\rm P(A \cup B) = 0.6\) and A and B occur simultaneously with a probability 0.3 ⇒ \(\rm P(A \cap B) = 0.3\) we know that, \(\rm P(A) +P(B) = P(A \cup B) + P(A \cap B)\) ⇒ \(\rm P(A) +P(B) = 0.6 + 0.3 = 0.9\) Also, we know that P(A') + P(B') = 1 - P(A) + 1 - P(B) ⇒ P(A') + P(B') = 2 - 0.9 ⇒ P(A') + P(B') = 1.1 Hence, For any two events A and B, the probability that at least one of them occur is 0.6. If A and B occur simultaneously with a probability 0.3, then P(A') + P(B') is 1.1

For any two events A and B, the probability that at least one of them occur is 0.6. If A and B occur simultaneously with a probability 0.3, then P(A') + P(B') is 1. 0.92. 1.153. 1.14. 1.0

Answer» Correct Answer - Option 3 : 1.1

Concept:

we know that,

\(\rm P(A) +P(B) = P(A \cup B) + P(A \cap B)\)

P(A') = 1 - P(A)

Calculations:

Given, For any two events A and B, the probability that at least one of them occur is 0.6

⇒ \(\rm P(A \cup B) = 0.6\)

and A and B occur simultaneously with a probability 0.3

⇒ \(\rm P(A \cap B) = 0.3\)

we know that,

\(\rm P(A) +P(B) = P(A \cup B) + P(A \cap B)\)

⇒ \(\rm P(A) +P(B) = 0.6 + 0.3 = 0.9\)

Also, we know that

P(A') + P(B') = 1 - P(A) + 1 - P(B)

⇒ P(A') + P(B') = 2 - 0.9

⇒ P(A') + P(B') = 1.1

Hence, For any two events A and B, the probability that at least one of them occur is 0.6. If A and B occur simultaneously with a probability 0.3, then P(A') + P(B') is 1.1

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