Let A and B be two events such that P(A ∪B)=(1)/(6), P(A ∩B)=(1)/(4) and P(A̅)=(1)/(4), where A̅

step 1 In this problem we are given that p of a union b not is given as 1 by 6 which means that p of a

Let A and B be two events such that P(A ∪B)=(1)/(6), P(A...

Let $A$ and $B$ be two events such that $P(\overline{A \cup B})=\frac{1}{6}, P(\overline{A \cap B})=\frac{1}{4}$ and $P(\bar{A})=\frac{1}{4}$, where $\bar{A}$ stands for the complement of the event $\mathrm{A}$. Then the events $\mathrm{A}$ and $\mathrm{B}$ are [Main 2014] (a) independent but not equally likely. (b) independent and equally likely. (c) mutually exclusive and independent. (d) equally likely but not independent.

Let $A$ and $B$ be two events such that $P(\overline{A \cup B})=\frac{1}{6}, P(\overline{A \cap B})=\frac{1}{4}$ and $P(\bar{A})=\frac{1}{4}$, where $\bar{A}$ stands for the complement of the event $\mathrm{A}$. Then the events $\mathrm{A}$ and $\mathrm{B}$ are [Main 2014]
(a) independent but not equally likely.
(b) independent and equally likely.
(c) mutually exclusive and independent.
(d) equally likely but not independent.

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Complement Rule and De Morgan's Laws

These fundamental principles relate the probability of an event to the probability of its complement (the event not occurring) and provide relationships between unions and intersections via complements. They are essential for translating given probabilities of complementary events into probabilities of the events themselves.

Inclusion?Exclusion Principle

This principle allows one to calculate the probability of the union of events by adding the probabilities of the individual events and then subtracting the probabilities of their intersections. It is crucial for solving problems where direct probabilities are not provided, but those of unions or intersections are given.

Independence of Events

Independence is a central concept in probability which states that two events are independent if the probability of their intersection equals the product of their individual probabilities. Checking this condition is key when determining whether two events have no influence on each other.

Equally Likely Events

This concept refers to situations where multiple events have the same probability of occurring. It is important when comparing events to determine if their chances are uniform or if one event is more likely than another.

Transcript

Please give Ace some feedback