A six-faced die is biased such that it is twi | vedclass

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

Question

(D) Let $P(O)$ be the probability of getting an odd number and $P(E)$ be the probability of getting an even number.Since the die is biased such that a

Vedclass · Accepted Answer

$\frac{5}{9}$

Vedclass · Answer

(D) Let $P(O)$ be the probability of getting an odd number and $P(E)$ be the probability of getting an even number.Since the die is biased such that an even number is twice as likely as an odd number, we have $P(E) = 2P(O)$.Since the sum of probabilities is $1$, $P(E) + P(O) = 1$, which gives $3P(O) = 1$, so $P(O) = \frac{1}{3}$ and $P(E) = \frac{2}{3}$.The sum of two numbers is even if both are even or both are odd.$P(	ext{Sum is even}) = P(E, E) + P(O, O)$.$P(E, E) = P(E) 	imes P(E) = \frac{2}{3} 	imes \frac{2}{3} = \frac{4}{9}$.$P(O, O) = P(O) 	imes P(O) = \frac{1}{3} 	imes \frac{1}{3} = \frac{1}{9}$.Therefore, $P(	ext{Sum is even}) = \frac{4}{9} + \frac{1}{9} = \frac{5}{9}$.

$A$ six-faced die is biased such that it is twice as likely to show an even number as an odd number when thrown. If it is thrown twice, what is the probability that the sum of the two numbers obtained is even?

Similar Questions

$A$ coin is tossed and a dice is rolled. The probability that the coin shows the head and the dice shows $6$ is

$5$ boys and $5$ girls are sitting in a row randomly. The probability that boys and girls sit alternatively is

In a single throw of $2$ dice, what is the probability of a doublet?

$A$ man is known to speak the truth $3$ out of $4$ times. He throws a die and reports that it is a six. The probability that it is actually a six,is

$A$ box contains $5$ green,$4$ yellow,and $3$ white marbles. Three marbles are drawn at random. What is the probability that they are not of the same colour?

Vedclass Test Series

Exam Paper Generator

Online Exam Module