Probability of (A and B, Intersection)

Probability of (A and B, Intersection)

How to find the probability of (A and B, intersection): meaning, example and its solution.

Meaning

P(A and B) means the probability of both events A and B happening.

P(A and B) means
the probability of
both events A and B happening.

So, to find P(A and B),

find n(S),
total number of ways,

find n(A and B),
the number of ways
of both A and B happening,

then find P(A and B):
P(A and B) = n(A and B) / n(S).

Probability

Example

Numbers from 1 to 10 are given. If you randomly pick a number, find P(odd and prime).

Numbers from 1 to 10 are given.

So there are 10 numbers
that can be picked.

So n(S) = 10.

Set the event A as
picking an odd number.

The odd numbers from 1 to 10 are
{1, 3, 5, 7, 9}.

And set the event B as
picking a prime number.

The prime numbers from 1 to 10 are
{2, 3, 5, 7}.

The numbers that are in both A and B are
{3, 5, 7}.

So [A and B] is
{3, 5, 7}.

[A and B] is {3, 5, 7}.

So n(A and B) = 3.

n(S) = 10
n(A and B) = 3

So P(A and B) = 3/10.

Probability