A and B are two independent events. The proba | vedclass

Name: PDF Generator App | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(a) $P(A \cap B) = P(A).P(B) = \frac{1}{6}$

$P(\bar A \cap \bar B) = \frac{1}{3} = 1 - P(A \cup B)$

$ \Rightarrow \frac{1}{3} = 1 - [P(A) + P(B)

Vedclass · Accepted Answer

$\frac{1}{2}$ and $\frac{1}{3}$

Vedclass · Answer

(a) $P(A \cap B) = P(A).P(B) = \frac{1}{6}$

$P(\bar A \cap \bar B) = \frac{1}{3} = 1 - P(A \cup B)$

$ \Rightarrow \frac{1}{3} = 1 - [P(A) + P(B)] + \frac{1}{6} $

$\Rightarrow P(A) + P(B) = \frac{5}{6}.$

Hence $P(A)$ and $P(B)$ are $\frac{1}{2}$ and $\frac{1}{3}.$

$A$ and $B$ are two independent events. The probability that both $A$ and $B$ occur is $\frac{1}{6}$ and the probability that neither of them occurs is $\frac{1}{3}$. Then the probability of the two events are respectively

Similar Questions

Events $E$ and $F$ are such that $P ( $ not $E$ not $F )=0.25,$ State whether $E$ and $F$ are mutually exclusive.

If $A$ and $B$ are two mutually exclusive events, then $P\,(A + B) = $

For two given events $A$ and $B$, $P\,(A \cap B) = $

Let ${E_1},{E_2},{E_3}$ be three arbitrary events of a sample space $S$. Consider the following statements which of the following statements are correct

Two events $A$ and $B$ will be independent, if