If A and B are two events such that P(A) = 0. | vedclass

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

Question

(A) Given: $P(A) = 0.7$,$P(B) = 0.4$,$P(A \cap \overline{B}) = 0.5$. First,find $P(A \cap B)$: $P(A) = P(A \cap B) + P(A \cap \overline{B}) \implies 0

Vedclass · Accepted Answer

$\frac{1}{4}$

Vedclass · Answer

(A) Given: $P(A) = 0.7$,$P(B) = 0.4$,$P(A \cap \overline{B}) = 0.5$. First,find $P(A \cap B)$: $P(A) = P(A \cap B) + P(A \cap \overline{B}) \implies 0.7 = P(A \cap B) + 0.5 \implies P(A \cap B) = 0.2$. Next,find $P(A \cup \overline{B})$: $P(A \cup \overline{B}) = P(A) + P(\overline{B}) - P(A \cap \overline{B}) = 0.7 + (1 - 0.4) - 0.5 = 0.7 + 0.6 - 0.5 = 0.8$. Now,calculate $P(B \mid (A \cup \overline{B}))$: $P(B \mid (A \cup \overline{B})) = \frac{P(B \cap (A \cup \overline{B}))}{P(A \cup \overline{B})} = \frac{P((B \cap A) \cup (B \cap \overline{B}))}{P(A \cup \overline{B})} = \frac{P(A \cap B) + 0}{0.8} = \frac{0.2}{0.8} = \frac{1}{4}$.

If $A$ and $B$ are two events such that $P(A) = 0.7$,$P(B) = 0.4$,and $P(A \cap \overline{B}) = 0.5$,where $\overline{B}$ denotes the complement of $B$,then $P(B \mid (A \cup \overline{B}))$ is equal to:

Similar Questions

Two events $A$ and $B$ are given. If $P(A) = \frac{1}{4}$,$P(A|B) = \frac{1}{2}$,and $P(B|A) = \frac{2}{3}$,then what is the value of $P(B)$?

Two numbers are selected at random from the set $\{1, 2, 3, \ldots, 13\}$. If the sum of the selected numbers is even,what is the probability that both the numbers are odd?

If $A$ and $B$ are two events such that $P(A) = \frac{3}{8}$,$P(B) = \frac{5}{8}$ and $P(A \cup B) = \frac{3}{4}$,then $P(A|B) = $

Find $P(E | F)$ for a coin tossed three times,where $E:$ at most two tails,$F:$ at least one tail. (in $/7$)

$A$ couple has two children. One of them is a boy. What is the probability that the other child is also a boy?

Vedclass Test Series

Exam Paper Generator

Online Exam Module