If two events A and B are such that P A C -0-3- P B -0-4- P A - B C -0-5- then find the value of P - B - A - B C-A-B-C- D- 1-2

The correct option is B P [ B/A ∪ B^C ]=P(B ∩ (A ∪ B^C)/P(A ∪ B^C)) =p(A ∩ B)/P(A)+P(B^C) P(A ∩ B^C) =P(A) P(A ∩ B^C)/P(A)+P(B^C) P(A ∩ B^C) =0.7 0.5/0.8=1/ ...

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Byju's Answer

Standard XII

Mathematics

Conditional Probability

If two events...

Question

If two events A and B are such that $P (A^{C}) = 0.3, P (B) = 0.4, P (A \cap B^{C}) = 0.5$ , then find the value of $P [\frac{B}{A \cup B^{C}}]$

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Solution

The correct option is B
$P [\frac{B}{A \cup B^{C}}] = \frac{P (B \cap (A \cup B^{C})}{P (A \cup B^{C}))} = \frac{p (A \cap B)}{P (A) + P (B^{C}) - P (A \cap B^{C})} = \frac{P (A) - P (A \cap B^{C})}{P (A) + P (B^{C}) - P (A \cap B^{C})} = \frac{0.7 - 0.5}{0.8} = \frac{1}{4}$

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If two events A and B are such that P(AC)=0.3,P(B)=0.4,P(A∩BC)=0.5, then find the value of P[BA∪BC]

The correct option is B P[BA∪BC]=P(B∩(A∪BC)P(A∪BC))=p(A∩B)P(A)+P(BC)−P(A∩BC)=P(A)−P(A∩BC)P(A)+P(BC)−P(A∩BC)=0.7−0.50.8=14

If two events A and B are such that $P (A^{C}) = 0.3, P (B) = 0.4, P (A \cap B^{C}) = 0.5$ , then find the value of $P [\frac{B}{A \cup B^{C}}]$

The correct option is B
$P [\frac{B}{A \cup B^{C}}] = \frac{P (B \cap (A \cup B^{C})}{P (A \cup B^{C}))} = \frac{p (A \cap B)}{P (A) + P (B^{C}) - P (A \cap B^{C})} = \frac{P (A) - P (A \cap B^{C})}{P (A) + P (B^{C}) - P (A \cap B^{C})} = \frac{0.7 - 0.5}{0.8} = \frac{1}{4}$