The probability for a contractor to get a roa | vedclass

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

Question

(C) Let $A$ be the event of getting a road contract and $B$ be the event of getting a building contract. Given: $P(A) = \frac{2}{9}$,$P(B) = \frac{5}{

Vedclass · Accepted Answer

$\frac{7}{18}$

Vedclass · Answer

(C) Let $A$ be the event of getting a road contract and $B$ be the event of getting a building contract. Given: $P(A) = \frac{2}{9}$,$P(B) = \frac{5}{9}$,and $P(A \cap B) = \frac{1}{6}$. We need to find the probability of getting neither contract,which is $P(A' \cap B') = P((A \cup B)')$. First,calculate the probability of getting at least one contract: $P(A \cup B) = P(A) + P(B) - P(A \cap B)$ $P(A \cup B) = \frac{2}{9} + \frac{5}{9} - \frac{1}{6} = \frac{7}{9} - \frac{1}{6}$ Finding a common denominator $(18)$: $P(A \cup B) = \frac{14}{18} - \frac{3}{18} = \frac{11}{18}$. Now,the probability of getting neither contract is: $P((A \cup B)') = 1 - P(A \cup B) = 1 - \frac{11}{18} = \frac{7}{18}$. Thus,the probability is $\frac{7}{18}$.

The probability for a contractor to get a road contract is $\frac{2}{9}$ and to get a building contract is $\frac{5}{9}$. If the probability to get both the contracts is $\frac{1}{6}$,then what is the probability to get neither of these two contracts?

Similar Questions

$P, Q$ and $R$ try to hit the same target one after the other. If their probabilities of hitting the target are $\frac{2}{3}, \frac{3}{5}, \frac{5}{7}$ respectively,then the probability that the target is hit by $P$ or $Q$ but not by $R$ is

In a non-leap year, the probability of getting $53$ Sundays or $53$ Tuesdays or $53$ Thursdays is:

Two friends $A$ and $B$ apply for a job in the same company. The probability of $A$ getting selected is $\frac{2}{5}$ and that of $B$ is $\frac{4}{7}$. Then the probability that one of them is selected is:

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

When two dice are thrown simultaneously,what is the probability that the sum of the numbers on the top faces is $5$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module