probability symbols examples

Example 1

With numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12

and A = multiples of 3 = 3, 6, 9, 12

and B = multiples of 4 = 4, 8, 12

1. If you picked one number out of a hat find P (A ∪ B).

Answer as follows: 

P (A ∪ B) - what is the probability of A OR B being picked.

We know probability = right answers divided by all the answers.

The only numbers that can be picked out of the hat that can be A or B are:

3 4 6 8 9 and 12 which we call the RIGHT (or correct) ones.

The probability therefore is:

`Probability = (6\text(  right))/(12\text(  all)) = 6/12`

Which is `0.5` probability.

Which is `50%` probability.

2. If you picked one number out of the hat find P (A ∩ B).

Answer as follows: 

P (A ∩ B) - what is the probability of event A and B happening.

There is only 1 number that satisfies this event which is 12.

We know probability = right answers divided by all the answers.

`Probability = (1\text(  right))/(12\text(  all)) = 1/12`

`Probability   is   1/12`

Which is `0.08dot3` probability

Which is `8.33%` probability

Example 2

In a deck of cards what is the probability of drawing a red card and a king card. i.e. what is P (red ∪ kings).

Answer as follows:

P (red ∪ kings) mean what is the probability of red OR kings being picked. 

Red cards are half the pack which is 26 cards.

King cards are four BUT two have already been used in the reds. 

We know probability = right answers divided by all the answers.

`Probability = (26 + 2)/52`

`Probability = 28/52`

`Probability = 7/13`

Which is `0.538` probability

Which is `5.38%`