The probability that at least one of A and B | vedclass

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

Question

(C) Given that the probability that at least one of $A$ and $B$ occurs is $P(A \cup B) = 0.6$. Also,the probability that $A$ and $B$ occur simultaneou

Vedclass · Accepted Answer

$1.1$

Vedclass · Answer

(C) Given that the probability that at least one of $A$ and $B$ occurs is $P(A \cup B) = 0.6$. Also,the probability that $A$ and $B$ occur simultaneously is $P(A \cap B) = 0.3$. We know that $P(A \cup B) = 1 - P(A' \cap B')$,so $P(A' \cap B') = 1 - 0.6 = 0.4$. Using De Morgan's Law,$P(A' \cap B') = P((A \cup B)')$. We need to find $P(A') + P(B')$. Using the formula $P(A' \cup B') = P(A') + P(B') - P(A' \cap B')$,we have: $P(A' \cup B') = P((A \cap B)') = 1 - P(A \cap B) = 1 - 0.3 = 0.7$. Substituting the values into the formula: $0.7 = P(A') + P(B') - 0.4$. Therefore,$P(A') + P(B') = 0.7 + 0.4 = 1.1$.

The probability that at least one of $A$ and $B$ occurs is $0.6$. If $A$ and $B$ occur simultaneously with probability $0.3$,then $P(A') + P(B') = $

Similar Questions

The probability that $A$ speaks truth is $4/5$,while the probability that $B$ speaks truth is $3/4$. The probability that $A$ and $B$ contradict each other when asked to reveal the fact is

$A$ die is thrown. Describe the following events: $A$: a number less than $7$,$B$: a number greater than $7$,$C$: a multiple of $3$. Find $B \cup C$.

Three athletes $A, B$ and $C$ participate in a race competition. The probability of winning for $A$ and $B$ is twice the probability of winning for $C$. Then the probability that the race is won by $A$ or $B$ is:

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

Three coins are tossed once. Find the probability of getting no head.

Vedclass Test Series

Exam Paper Generator

Online Exam Module