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 probabilities of a student getting $I, II$ and $III$ division in an examination are respectively $\frac{1}{10}, \frac{3}{5}$ and $\frac{1}{4}$. The probability that the student fails in the examination is

In a random experiment of selecting a ticket from $50$ tickets numbered $00, 01, 02, 03, ..., 47, 49$,if a ticket is selected such that the product of its digits is $0$,what is the probability that the sum of its digits is $8$?

$A$ card is drawn at random from a well-shuffled pack of $52$ cards. The probability of getting a two of hearts or diamonds is

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

The event $A$ is independent of itself if and only if $P(A) = $

Vedclass Test Series

Exam Paper Generator

Online Exam Module