If an integer is chosen at random from the fi | vedclass

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

Question

(B) Let $A$ be the event that the chosen number is a multiple of $4$,and $B$ be the event that the chosen number is a multiple of $6$.The number of mu

Vedclass · Accepted Answer

$\frac{33}{100}$

Vedclass · Answer

(B) Let $A$ be the event that the chosen number is a multiple of $4$,and $B$ be the event that the chosen number is a multiple of $6$.The number of multiples of $4$ in the first $100$ integers is $\frac{100}{4} = 25$. So,$P(A) = \frac{25}{100}$.The number of multiples of $6$ in the first $100$ integers is $\lfloor \frac{100}{6} floor = 16$. So,$P(B) = \frac{16}{100}$.The multiples of both $4$ and $6$ are multiples of $	ext{lcm}(4, 6) = 12$. The number of multiples of $12$ in the first $100$ integers is $\lfloor \frac{100}{12} floor = 8$. So,$P(A \cap B) = \frac{8}{100}$.Using the addition theorem of probability,the required probability is:$P(A \cup B) = P(A) + P(B) - P(A \cap B)$$P(A \cup B) = \frac{25}{100} + \frac{16}{100} - \frac{8}{100} = \frac{33}{100}$.

If an integer is chosen at random from the first $100$ positive integers,then the probability that the chosen number is a multiple of $4$ or $6$ is:

Similar Questions

If $A$ and $B$ are arbitrary events,then

The probability that $A$ speaks the truth is $\frac{4}{5}$,while the probability that $B$ speaks the truth is $\frac{3}{4}$. What is the probability that they contradict each other when asked to speak on a fact?

If a card is drawn at random from a well-shuffled pack of $52$ playing cards,then the probability that it is either an ace or a spade card is

One of the two events must occur. If the chance of one is $\frac{2}{3}$ of the other,then the odds in favour of the other are

The odds in favour of drawing a king from a pack of $52$ playing cards is

Vedclass Test Series

Exam Paper Generator

Online Exam Module