If a number is selected from the first 30 nat | vedclass

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

Question

(D) The set of the first $30$ natural numbers is $S = \{1, 2, 3, \dots, 30\}$, so the total number of outcomes is $n(S) = 30$. Let $A$ be the event th

Vedclass · Accepted Answer

$\frac{1}{3}$

Vedclass · Answer

(D) The set of the first $30$ natural numbers is $S = \{1, 2, 3, \dots, 30\}$, so the total number of outcomes is $n(S) = 30$. Let $A$ be the event that the number is divisible by $4$. The numbers are $\{4, 8, 12, 16, 20, 24, 28\}$, so $n(A) = 7$. Let $B$ be the event that the number is divisible by $7$. The numbers are $\{7, 14, 21, 28\}$, so $n(B) = 4$. The event $A \cap B$ represents numbers divisible by both $4$ and $7$ (i.e.,divisible by $28$). The only number is $\{28\}$, so $n(A \cap B) = 1$. Using the addition theorem of probability, $P(A \cup B) = P(A) + P(B) - P(A \cap B)$. $P(A \cup B) = \frac{7}{30} + \frac{4}{30} - \frac{1}{30} = \frac{10}{30} = \frac{1}{3}$.

If a number is selected from the first $30$ natural numbers, then the probability that the number selected is divisible by $4$ or $7$ is:

Similar Questions

Three critics review a book. For the three critics,the odds in favour of the book are $(5: 2)$,$(4: 3)$ and $(3: 4)$ respectively. The probability that the majority is in favour of the book is

$A$ speaks the truth in $75\%$ of cases and $B$ speaks the truth in $80\%$ of cases. What is the probability that they contradict each other in stating the same fact?

$A, B, C$ are three events,one of which must and only one can happen. The odds in favour of $A$ are $4:6$,and the odds against $B$ are $7:3$. Then,the odds against $C$ are:

Given two mutually exclusive events $A$ and $B$ such that $P(A) = 0.45$ and $P(B) = 0.35,$ then $P(A \text{ or } B) =$

If the probability of $X$ to fail in the examination is $0.3$ and that for $Y$ is $0.2$,then the probability that either $X$ or $Y$ fail in the examination is

Vedclass Test Series

Exam Paper Generator

Online Exam Module