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Question Number 76588 by Rio Michael last updated on 28/Dec/19

Given three events A, B, and C sucb that

P (A) = P (C), P (A \cap C) = \frac{1}{10}, P (A \cup C) = \frac{1}{2}

P (C ∣ B) = \frac{2}{7}, P (B \cup C) = \frac{4}{5} find

a) P (A)

b) P (B)

Answered by john santu last updated on 28/Dec/19

a) c o n s i d e r P (A \cup C) = P (A) + P (C) - P (A \cap C)

\frac{1}{2} = 2 P (A) - \frac{1}{10} \to P (A) = \frac{3}{10}

Answered by john santu last updated on 28/Dec/19

b) P (B \cup C) = P (B) + P (C) - P (B / C) \times P (B)

\frac{4}{5} = P (B) + \frac{3}{10} - \frac{2}{7} \times P (B)

P (B) = (\frac{8}{10} - \frac{3}{10}) \times \frac{7}{5} = \frac{7}{10}

Commented by Rio Michael last updated on 28/Dec/19

thanks