AND / OR
If you want to calculate the probability of an event happening AND another event
happening, the probability will be smaller than the original, single event. This makes
sense if you think about it. The probability of England winning the World Cup AND
the European Cup must be less likely than just winning one of them.
To calculate the probability of an event AND another (independent) event, we
MULTIPLY them together. This will make the total probability smaller (e.g. ½ x ½ =
¼.)
Similarly, to calculate the probability of an event OR another (mutually exclusive)
event, we ADD them together. This will make the total probability larger (e.g. ¼ + ¼
=½)
You should be confident with adding and multiplying fractions before attempting
this.
Work out the following probabilities:
Medium
Easy
1. Rolling 2 sixes on a dice
2. Rolling 3 fours on a dice
3. Flipping a coin and getting 2 tails
in a row
4. Winning 2 games of “scissors,
paper, stone” in a row
5. A toaster burning toast three
times in a row, if the probability of
burning is 0.3
6. Rolling a six or a four on a dice
7. Rolling 3 fours or 3 fives on a dice
8. Flipping a coin and getting either 2
tails in a row or 2 heads in a row
9. Winning 2 games of “scissors,
paper, stone” in a row, or drawing
them both.
10. Burning toast three times in a row,
or not burning it three times in a
row (from Q5)
1.
2.
3.
4.
Rolling a six on a dice and then drawing a jack from a deck of cards
Rolling a prime number on a dice and then drawing a heart from a deck of cards
Getting tails when flipping a coin, and then rolling a number less than 3 on a dice.
Winning “rock paper scissors” and then drawing an ace of spades from a deck of
cards.
5. Picking a male Simpson from the Simpson family at random, and then rolling a
number greater than 4 on a dice.
Find 𝑃(𝐴 ∩ 𝐵) 𝑎𝑛𝑑 𝑃(𝐴 ∪ 𝐵) for each of the following:
(Assume independence for 𝑃(𝐴 ∩ 𝐵) and mutual exclusivity for 𝑃(𝐴 ∪ 𝐵)
1
2
Hard
1. 𝑃(𝐴) = 4 𝑃(𝐵) = 3
1
2. 𝑃(𝐴) = 3 𝑃(𝐵) = 0.2
1
3. 𝑃(𝐴) = 12 𝑃(𝐵) = 40%
7
4. 𝑃(𝐴) = 12 𝑃(𝐵) = 0.02
5. 𝑃(𝐴) =
6. 𝑃(𝐴) =
𝑎
9
𝑎2
4
2
𝑃(𝐵) = 𝑦
𝑃(𝐵) = 0.2
5
7. 𝑃(𝐴) = 12% 𝑃(𝐵) = 𝑝
2
8. 𝑃(𝐴) = 0.15 𝑃(𝐵) = 3