Table of Contents

- 1 Is event A is subset of event B then?
- 2 How do you find the probability of the events if event A is a subset of event B?
- 3 How do you calculate Union probability?
- 4 What is the probability of B given a?
- 5 What is the probability of A if B?
- 6 What is the probability of a union B?
- 7 Is a subset of B and A is not equal to B then?
- 8 What is the probability of A and B?
- 9 How do you find the probability that a ⊂ B?
- 10 What is the formula for disjoint and independent events?

## Is event A is subset of event B then?

Given A is a subset of B ==>AnB = A.B = A .

## How do you find the probability of the events if event A is a subset of event B?

Rule 3: If two events A and B are disjoint, then the probability of either event is the sum of the probabilities of the two events: P(A or B) = P(A) + P(B).

**What is if A is subset of B?**

If set A is the subset of set B, it means that all the elements of set A are present in set B. Also A – B means elements of set A which are not present in set B.

### How do you calculate Union probability?

Union is denoted by the symbol ∪ . The general probability addition rule for the union of two events states that P(A∪B)=P(A)+P(B)−P(A∩B) P ( A ∪ B ) = P ( A ) + P ( B ) − P ( A ∩ B ) , where A∩B A ∩ B is the intersection of the two sets.

### What is the probability of B given a?

This probability is written P(B|A), notation for the probability of B given A. In the case where events A and B are independent (where event A has no effect on the probability of event B), the conditional probability of event B given event A is simply the probability of event B, that is P(B). P(A and B) = P(A)P(B|A).

**What is the probability of A or B?**

The probability of two disjoint events A or B happening is: p(A or B) = p(A) + p(B).

#### What is the probability of A if B?

If A and B are two events in a sample space S, then the conditional probability of A given B is defined as P(A|B)=P(A∩B)P(B), when P(B)>0.

#### What is the probability of a union B?

The general probability addition rule for the union of two events states that P(A∪B)=P(A)+P(B)−P(A∩B) P ( A ∪ B ) = P ( A ) + P ( B ) − P ( A ∩ B ) , where A∩B A ∩ B is the intersection of the two sets. The addition rule can be shortened if the sets are disjoint: P(A∪B)=P(A)+P(B) P ( A ∪ B ) = P ( A ) + P ( B ) .

**When A is subset of B and B is a subset of A?**

In mathematics, set A is a subset of a set B if all elements of A are also elements of B; B is then a superset of A. It is possible for A and B to be equal; if they are unequal, then A is a proper subset of B. The relationship of one set being a subset of another is called inclusion (or sometimes containment).

## Is a subset of B and A is not equal to B then?

If A is a subset of B (A ⊆ B), but A is not equal to B, then we say A is a proper subset of B, written as A ⊂ B or A ⊊ B. The following diagram shows an example of subset.

## What is the probability of A and B?

The probability of A and B means that we want to know the probability of two events happening at the same time. There’s a couple of different formulas, depending on if you have dependent events or independent events. Formula for the probability of A and B (independent events): p(A and B) = p(A) * p(B).

**Are the events A and B independent events?**

The probability that one event (P (A)) occurs in no way affects the probability of the other event occurring (P (B)) here. So from the definition of the independent events, A and B are independent. But it looks like there is some dependency between A and B because A is a subset of B. A always occurs where B occurs.

### How do you find the probability that a ⊂ B?

Assuming B has happened affects that probability that A has happened, hence they are not independent. In general, if A ⊂ B we have P (A | B) = P (A ∩ B) P (B) = P (A) P (B). In your example, this would be 0.2 0.3 = 2 3, as expected.

### What is the formula for disjoint and independent events?

You probably learned a fact on the lines of “if two events X and Y are disjoint and independent, then P ( X ∪ Y) = P ( X) + P ( Y) .” Since A and A c ∩ B are disjoint, you have