For three events $A$, $B$, and $C$ of a sample space, $P(\text{exactly one of } A \text{ or } B \text{ occurs}) = P(\text{exactly one of } B \text{ or } C \text{ occurs}) = P(\text{exactly one of } C \text{ or } A \text{ occurs}) = \frac{1}{4}$. If the probability of all the three events occurring simultaneously is $\frac{1}{16}$, then the probability that at least one of the events occurs is:
- A$\frac{3}{16}$
- B$\frac{5}{16}$
- C$\frac{7}{16}$
- D$\frac{7}{32}$
Explore More
Similar Questions
If $A$ and $B$ are independent events of a random experiment such that $P(A \cap B) = \frac{1}{6}$ and $P(\bar{A} \cap \bar{B}) = \frac{1}{3}$,then $P(A)$ is equal to (Here,$\bar{E}$ is the complement of the event $E$)
DifficultTS EAMCET 2008
View SolutionLet $S = \{w_1, w_2, \ldots\}$ be the sample space associated with a random experiment. Let $P(w_n) = \frac{P(w_{n-1})}{2}$ for $n \geq 2$. Let $A = \{2k + 3\ell : k, \ell \in \mathbb{N}\}$ and $B = \{w_n : n \in A\}$. Then $P(B)$ is equal to:
DifficultJEE MAIN 2023
View SolutionTwo distinct numbers $a$ and $b$ are chosen randomly from the set $S = \{2^1, 2^2, 2^3, \dots, 2^{25}\}$. What is the probability that $\log_2(ab)$ is an integer?
If $P(A') + P(B') P(A \cup B) = 0.7$,then $P(A') + P(B')$ is
Two players,$P_1$ and $P_2$,play a game against each other. In every round,each player rolls a fair die once. Let $x$ and $y$ denote the outcomes for $P_1$ and $P_2$. If $x > y$,$P_1$ scores $5$ points and $P_2$ scores $0$. If $x = y$,each scores $2$ points. If $x < y$,$P_1$ scores $0$ and $P_2$ scores $5$. Let $X_n$ and $Y_n$ be the total scores of $P_1$ and $P_2$ after $n$ rounds. Match the following:
List-$I$ List-$II$ $(I)$ Probability of $(X_2 \geq Y_2)$ is $(P)$ $\frac{3}{8}$ $(II)$ Probability of $(X_2 > Y_2)$ is $(Q)$ $\frac{11}{16}$ $(III)$ Probability of $(X_3 = Y_3)$ is $(R)$ $\frac{5}{16}$ $(IV)$ Probability of $(X_3 > Y_3)$ is $(S)$ $\frac{355}{864}$ $(T)$ $\frac{77}{432}$
| List-$I$ | List-$II$ |
| $(I)$ Probability of $(X_2 \geq Y_2)$ is | $(P)$ $\frac{3}{8}$ |
| $(II)$ Probability of $(X_2 > Y_2)$ is | $(Q)$ $\frac{11}{16}$ |
| $(III)$ Probability of $(X_3 = Y_3)$ is | $(R)$ $\frac{5}{16}$ |
| $(IV)$ Probability of $(X_3 > Y_3)$ is | $(S)$ $\frac{355}{864}$ |
| $(T)$ $\frac{77}{432}$ |
Vedclass Products
For Students
Vedclass Test Series
Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.
Start Free TrialFor Teachers
Exam Paper Generator
Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.
Try FreeFor Institutes
Online Exam Module
Live online exams with unlimited students, 360° analytics & white-label branding.
See Demo