A die marked 1,,2,,3 in red and 4,,5,,6 in gr | vedclass

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

Question

When a die is thrown, the sample space ( $S$ ) is

$\mathrm{S}=\{1,2,3,4,5,6\}$

Let $A:$ the number is even $=\{2,4,6\}$

$\Rightarrow P(A)=\fr

Vedclass · Accepted Answer

Vedclass · Answer

When a die is thrown, the sample space ( $S$ ) is

$\mathrm{S}=\{1,2,3,4,5,6\}$

Let $A:$ the number is even $=\{2,4,6\}$

$\Rightarrow P(A)=\frac{3}{6}=\frac{1}{2}$

$B:$ the number is red $=\{1,2,3\}$

$\Rightarrow P(B)=\frac{3}{6}=\frac{1}{2}$

$	herefore $ $A \cap B=\{2\}$

$P(A B)=P(A \cap B)=\frac{1}{6}$

$P(A) P(B)=\frac{1}{2} 	imes \frac{1}{2}=\frac{1}{4} 
eq \frac{1}{6}$

$\Rightarrow $  $P(A) \cdot P(B) 
eq P(A B)$

Therefore, $A$ bad $B$ are not independent.

A die marked $1,\,2,\,3$ in red and $4,\,5,\,6$ in green is tossed. Let $A$ be the event, $'$ the number is even,$'$ and $B$ be the event, 'the number is red'. Are $A$ and $B$ independent?

Similar Questions

Two dice are thrown. What is the probability that the sum of the numbers appearing on the two dice is $11$, if $5$ appears on the first

If $E$ and $F$ are independent events such that $0 < P(E) < 1$ and $0 < P\,(F) < 1,$ then

If the odds against an event be $2 : 3$, then the probability of its occurrence is

Two balls are drawn at random with replacement from a box containing $10$ black and $8$ red balls. Find the probability that One of them is black and other is red.

If two events $A$ and $B$ are such that $P\,(A + B) = \frac{5}{6},$ $P\,(AB) = \frac{1}{3}\,$ and $P\,(\bar A) = \frac{1}{2},$ then the events $A$ and $B$ are