Suppose that a die (with faces marked 1 to 6) | vedclass

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

Question

(B) Let $P(K)$ be the probability of getting face $K$. Since $P(K) \propto K$,we have $P(K) = cK$ for some constant $c$.Since the sum of all probabili

Vedclass · Accepted Answer

$\frac{4}{7}$

Vedclass · Answer

(B) Let $P(K)$ be the probability of getting face $K$. Since $P(K) \propto K$,we have $P(K) = cK$ for some constant $c$.Since the sum of all probabilities must be $1$,we have $\sum_{K=1}^{6} cK = 1$.$c(1 + 2 + 3 + 4 + 5 + 6) = 1 \implies 21c = 1 \implies c = \frac{1}{21}$.The outcomes that are even numbers are $2, 4, 6$.The probability of getting an even number is $P(2) + P(4) + P(6) = c(2 + 4 + 6) = 12c$.Substituting $c = \frac{1}{21}$,we get $\frac{12}{21} = \frac{4}{7}$.

Similar Questions

The probability that a number selected at random from the set of numbers $(1, 2, 3, \ldots, 100)$ is a cube,is

One card is drawn at random from a well-shuffled pack of $52$ cards. The probability that the card drawn is a face card (Jack,Queen,and King only) is

$A$ mathematics problem is given to three students $A, B$,and $C$. The probabilities of them solving the problem are $1/2, 1/3$,and $1/4$ respectively. What is the probability that the problem is solved?

In a single throw of two dice,the probability of getting a sum of more than $7$ is

When a pair of six-faced fair dice are thrown, the probability that the sum of the numbers on the two dice is greater than $7$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module