A fair die is thrown at random. Let A be the | vedclass

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

Question

(B) The sample space of a fair die is $S = \{1, 2, 3, 4, 5, 6\}$, so $n(S) = 6$.Event $A$: Number is a non-even prime number. The only non-even prime

Vedclass · Accepted Answer

$T, F$

Vedclass · Answer

(B) The sample space of a fair die is $S = \{1, 2, 3, 4, 5, 6\}$, so $n(S) = 6$.Event $A$: Number is a non-even prime number. The only non-even prime number on a die is $3$ and $5$. Thus, $A = \{3, 5\}$ and $n(A) = 2$.$P(A) = \frac{n(A)}{n(S)} = \frac{2}{6} = \frac{1}{3}$. Thus, statement $p$ is True $(T)$.Event $B$: Number is an odd number. Thus, $B = \{1, 3, 5\}$ and $n(B) = 3$.$P(B) = \frac{n(B)}{n(S)} = \frac{3}{6} = \frac{1}{2}$.Intersection $A \cap B$: The numbers in both $A$ and $B$ are $\{3, 5\}$, so $n(A \cap B) = 2$.$P(A \cap B) = \frac{2}{6} = \frac{1}{3}$.For $A$ and $B$ to be independent, $P(A \cap B) = P(A) 	imes P(B)$ must hold.$P(A) 	imes P(B) = \frac{1}{3} 	imes \frac{1}{2} = \frac{1}{6}$.Since $\frac{1}{3} 
eq \frac{1}{6}$, $P(A \cap B) 
eq P(A) 	imes P(B)$. Thus, statement $q$ is False $(F)$.The truth values are $T, F$.

Similar Questions

Three coins are tossed once. Let $A$ denote the event 'three heads show',$B$ denote the event 'two heads and one tail show',$C$ denote the event 'three tails show' and $D$ denote the event 'a head shows on the first coin'. Which events are compound?

An integer is chosen from the set $\{2k \mid -9 \leq k \leq 10\}$. The probability that the chosen integer is divisible by both $4$ and $6$ is

If $A$ and $B$ are any two events,then the probability that exactly one of them occurs is

One card is drawn from a well-shuffled deck of $52$ cards. If each outcome is equally likely,calculate the probability that the card will not be a black card.

When two dice are rolled,what is the probability that the sum of the numbers on the faces is a multiple of $4$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module