MUTUALLY EXCLUSIVE EVENTS Events are mutually exclusive if

• Events are mutually exclusive if they cannot happen at the same time.

• If A and B are mutually exclusive events then the probability of

Example 1 • What is the probability of a die showing a 2 or

Practice • The probabilities of three teams A, B and C winning a badminton

Solution/s c) P(none will win) = 1 – P(A or B or C will

Independent Events • Events are independent if the outcome of one event does not

Example 1 • If a dice is thrown twice, find the probability of getting

Two sets of cards with a letter on each card as follows are placed

Solution for no. 2 a) Probability that she picked J and R = b)

Example 3 • Two fair dice, one colored white and one colored red, are

Solution for No. 3 a) Probability the red die shows 2 and white die

DEPENDENT EVENTS • Events are dependent if the outcome of one event affects the

• If A and B are dependent events, then the probability of A

Example 1 • A purse contains four P 50 bills, five P 100 bills

• There are four P 50 bills. • There a total of twelve

• P(P 50, then P 50) = P(P 50) · P(P 50 after

Dependent: Practice • A bag contains 6 red, 5 blue and 4 yellow marbles.

Independent Events: Practice • Two fair dice, one colored white and one colored red,

Mutually Exclusive. Events: Practice • The probabilities of three teams A, B and C

Slides: 20

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MUTUALLY EXCLUSIVE EVENTS

• Events are mutually exclusive if they cannot happen at the same time. For example, if we toss a coin, either heads or tails might turn up, but not heads and tails at the same time. Similarly, in a single throw of a die, we can only have one number shown at the top face. The numbers on the face are mutually exclusive events

• If A and B are mutually exclusive events then the probability of A happening OR the probability of B happening is P(A) + P(B). • P(A or B) = P(A) + P(B)

Example 1 • What is the probability of a die showing a 2 or a 5?

Practice • The probabilities of three teams A, B and C winning a badminton competition are • • • Calculate the probability that a) either A or B will win b) either A or B or C will win c) none of these teams will win d) neither A nor B will win

Solution/s c) P(none will win) = 1 – P(A or B or C will win) d) P(neither A nor B will win) = 1 – P(either A or B will win)

Independent Events • Events are independent if the outcome of one event does not affect the outcome of another. For example, if you throw a die and a coin, the number on the die does not affect whether the result you get on the coin. • If A and B are independent events, then the probability of A happening AND the probability of B happening is P(A) × P(B). • P(A and B) = P(A) × P(B)

Example 1 • If a dice is thrown twice, find the probability of getting two 5’s.

Two sets of cards with a letter on each card as follows are placed into separate bags. Sara randomly picked one card from each bag. Find the probability that: a) She picked the letters ‘J’ and ‘R’. b) Both letters are ‘L’. c) Both letters are vowels.

Solution for no. 2 a) Probability that she picked J and R = b) Probability that both letters are L = c) Probability that both letters are vowels =

Example 3 • Two fair dice, one colored white and one colored red, are thrown. Find the probability that: • a) the score on the red die is 2 and white die is 5. • b) the score on the white die is 1 and red die is even

Solution for No. 3 a) Probability the red die shows 2 and white die 5 = b) Probability the white die shows 1 and red die shows an even number =

DEPENDENT EVENTS • Events are dependent if the outcome of one event affects the outcome of another. For example, if you draw two colored balls from a bag and the first ball is not replaced before you draw the second ball then the outcome of the second draw will be affected by the outcome of the first draw.

• If A and B are dependent events, then the probability of A happening AND the probability of B happening, given A, is P(A) × P(B after A). • P(A and B) = P(A) × P(B after A) • P(B after A) can also be written as P(B | A) • then P(A and B) = P(A) × P(B | A)

Example 1 • A purse contains four P 50 bills, five P 100 bills and three P 20 bills. Two bills are selected without the first selection being replaced. Find P(P 50, then P 50)

• There are four P 50 bills. • There a total of twelve bills. • P(P 50) = 4/12 • The result of the first draw affected the probability of the second draw. • There are three P 50 bills left. • There a total of eleven bills left. • P(P 50 after P 50) = 3/11

• P(P 50, then P 50) = P(P 50) · P(P 50 after P 50) = (4/12)x(3/11)=12/132 • The probability of drawing a P 50 bill and then a P 50 bill is

Dependent: Practice • A bag contains 6 red, 5 blue and 4 yellow marbles. Two marbles are drawn, but the first marble drawn is not replaced. • a) Find P(red, then blue). • b) Find P(blue, then blue)

Independent Events: Practice • Two fair dice, one colored white and one colored red, are thrown. Find the probability that: • a) the score on the red die is 2 and white die is 5. • b) the score on the white die is 1 and red die is even

Mutually Exclusive. Events: Practice • The probabilities of three teams A, B and C winning a badminton competition are • • • Calculate the probability that a) either A or B will win b) either A or B or C will win c) none of these teams will win d) neither A nor B will win