If A and B are two mutually exclusive and exhaustive events with P(B)

1.	If A and B are two mutually exclusive and exhaustive events with P(B) = 3 P(A), then what is the value of P(\(\bar B\))?(a) \(\frac{3}{4}\)(b) \(\frac{1}{4}\)(c) \(\frac{1}{3}\)(d) \(\frac{2}{3}\)
Answer» (b) \(\frac{1}{4}\) Since P(A) and P(B) are two mutually exclusive and exhaustive events , P(A) + P(B) = 1 \(\Rightarrow\) P(A) + 3 P(A) = 1 \(\Rightarrow\) 4 P(A) = 1 \(\Rightarrow\) P(A) = \(\frac{1}{4}\) \(\Rightarrow\) P(B) = 1- \(\frac{1}{4}\) = \(\frac{3}{4}\) \(\Rightarrow\) P(\(\bar B\)) = 1 - \(\frac{3}{4}\) = \(\frac{1}{4}\).

If A and B are two mutually exclusive and exhaustive events with P(B) = 3 P(A), then what is the value of P(\(\bar B\))?(a) \(\frac{3}{4}\)(b) \(\frac{1}{4}\)(c) \(\frac{1}{3}\)(d) \(\frac{2}{3}\)

Answer»

(b) \(\frac{1}{4}\)

Since P(A) and P(B) are two mutually exclusive and exhaustive events , P(A) + P(B) = 1

\(\Rightarrow\) P(A) + 3 P(A) = 1

\(\Rightarrow\) 4 P(A) = 1 \(\Rightarrow\) P(A) = \(\frac{1}{4}\)

\(\Rightarrow\) P(B) = 1- \(\frac{1}{4}\) = \(\frac{3}{4}\)

\(\Rightarrow\) P(\(\bar B\)) = 1 - \(\frac{3}{4}\) = \(\frac{1}{4}\).

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If A and B are two mutually exclusive and exhaustive events with P(B) = 3 P(A), then what is the value of P(\(\bar B\))?(a) \(\frac{3}{4}\)(b) \(\frac{1}{4}\)(c) \(\frac{1}{3}\)(d) \(\frac{2}{3}\)

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