A problem in Statistics is given to four stud | vedclass

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

Question

(B) Let $P(A), P(B), P(C),$ and $P(D)$ be the probabilities of students $A, B, C,$ and $D$ solving the problem respectively.Given: $P(A) = \frac{1}{3}

Vedclass · Accepted Answer

$\frac{2}{3}$

Vedclass · Answer

(B) Let $P(A), P(B), P(C),$ and $P(D)$ be the probabilities of students $A, B, C,$ and $D$ solving the problem respectively.Given: $P(A) = \frac{1}{3}, P(B) = \frac{1}{4}, P(C) = \frac{1}{5}, P(D) = \frac{1}{6}$.The probability that a student fails to solve the problem is $1 - P(	ext{solving})$.$P(A') = 1 - \frac{1}{3} = \frac{2}{3}$$P(B') = 1 - \frac{1}{4} = \frac{3}{4}$$P(C') = 1 - \frac{1}{5} = \frac{4}{5}$$P(D') = 1 - \frac{1}{6} = \frac{5}{6}$Since the events are independent,the probability that none of them solve the problem is $P(A') 	imes P(B') 	imes P(C') 	imes P(D') = \frac{2}{3} 	imes \frac{3}{4} 	imes \frac{4}{5} 	imes \frac{5}{6} = \frac{2}{6} = \frac{1}{3}$.The probability that the problem will be solved is $1 - P(	ext{none solve}) = 1 - \frac{1}{3} = \frac{2}{3}$.

$A$ problem in Statistics is given to four students $A, B, C$ and $D$. Their chances of solving it are $\frac{1}{3}, \frac{1}{4}, \frac{1}{5}$ and $\frac{1}{6}$ respectively. What is the probability that the problem will be solved?

Similar Questions

Out of $40$ consecutive natural numbers,two are chosen at random. The probability that the sum of the numbers is odd is:

$10$ coins are tossed. What is the probability that exactly $5$ heads appear?

$1$ bag contains $4$ white and $2$ black balls. Another bag contains $3$ white and $5$ black balls. If $1$ ball is drawn from each bag,find the probability that $1$ ball is white and $1$ ball is black.

In a box,there are $2$ red,$3$ black,and $4$ white balls. If three balls are drawn together,what is the probability that the balls drawn are of the same colour?

When two dice are rolled,what is the probability that the sum of the numbers appearing is $\leq 10$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module