Mutually Exclusive Events What does ‘Mutually Exclusive’ mean? Ask pupils for their own example of a mutually exclusive event Ask pupils for an example of events that aren’t mutually exclusive.. Eg drawing a king and a heart from a deck of cards For example, turning left and turning right at the same time. Or going to Liverpool at 9am tomorrow, and going to Manchester at 9am tomorrow Drawing an ace and a king from a deck

When events have no outcomes in common they are mutually exclusive. P(A  B) = 0 E.G. Getting a 2 or a 3 in one roll of a dice. A B S 1 6 1 6 4 6

When deciding if 2 events are mutually exclusive ask yourself the question: Can these events happen at the same time?

Mutually Exclusive Events Which of the following are mutually exclusive events? (a) A thumb tack falling head down and a thumb tack falling head up. (b) A student studying Maths and Physics. (c) Getting both a head and a tail when tossing a coin. (d) Getting a six and a two when throwing a dice. (e) Getting a king and a club when picking a card from a pack of playing cards.

Winning a football match Q1 Winning a football match AND Loosing the same football match

Q2 Getting the bus AND Missing the bus

Watching an Romance DVD Q3 Watching a comedy DVD AND Watching an Romance DVD

Q4 Being asleep AND Being awake

Rolling a number less than 3 Q5 Rolling a 2 AND Rolling a number less than 3

A traffic light being red Q6 A traffic light being red AND The traffic light being green

The same baby being a girl Q8 A baby being a boy AND The same baby being a girl

Randomly picking a dog from the pound Q9 AND The dog being Black

Me not winning the lottery Q10 AND My Friend not winning the lottery

We use the addition rule for ‘or’ and ‘union’ questions probabilities P(AB) = P(A) + P(B) - P(A  B) With all these questions it is good practice to draw a Venn diagram

Using the addition Rule A and B are 2 events such that P(A) = 0.8 and the P(B) = 0.5 where P(A n B) is 0.3. Find P(A U B) Are A and B mutually exclusive? Explain your answer.

Question If A and B are mutually exclusive events where P(A) = 0.4 and P(B) = 0.2. Find P(A U B)

Question A card is drawn from a deck of 52 cards. What is the probability that the card is a red card or a queen? What is the probability that the card is a club or a king?

Independent Events

When 2 events have no effect on each other they are called independent events. Examples of Independent events Getting a 5 on a spinner numbered 1,2,3,4,5,5,7,8 and a 3 on a fair unbiased dice. Flipping a coin and rolling a dice Spinning a spinner and Rolling a dice A B

Hint: If it is replaced then it is independent (No effect Probabilities remain the same) If it is not replaced then it is not independent.

Example A box contains 2 red counters and 4 yellow counters. One counter is picked at random and is not replaced What is the probability of picking a red counter on: The 1st pick The 2nd pick

The Multiplication Rule For events which use the word AND we use the multiplication rule P(A  B) = P(A) x P(B)

Question: When 2 dice are thrown what is the probability of getting 4 or more on each die 2 sixes

Question A gambler must throw a 6 with a single die to win a prize. Find the probability that he wins on the 3rd attempt

Find the probability that: Question A bag contains 5 red discs and 3 blue discs. A disc is selected at random and is not replaced. Find the probability that: The 1st 2 discs are Red? The 1st 2 discs are blue? The first 2 discs are not blue?

NOTE: If a question says ‘at least one’ then we must use the following ‘At Least one’ Questions NOTE: If a question says ‘at least one’ then we must use the following 1 – (Probability of the event not happening)

If we you are asked to investigate whether 2 events are independent. We use the formula P(A  B) = P(A) x P(B) and do the following: Find the left hand side: P(A  B) Find the right hand side: P(A) x P(B) If they are independent the left hand side will equal the right hand side

We can also prove 2 events are independent if we can prove that P(A|B) = P(A) P(B|A) = P(B)