OR b) Find the probability that he wins only one game a) Find the probability that he wins both games a) P(W,W) = 0.16 b) P(Wins once) = 0.24 + 0.24 = 0.48 P(W,W) = 0.4 x 0.4 = 0.16 0.6 P(W,N) = 0.4 x 0.6 = 0.24 OR P(N,W) = 0.6 x 0.4 = 0.24 0.4 0.6 0.6 P(N,N) = 0.6 x 0.6 = 0.36

b) Find the probability that at least one is at school a) Neither is at school b) P(at least one A) = 0.42 + 0.18 + 0.12 = 0.72 a) P(D,D) = 0.12 0.7 Attends P(A,A) = 0.6 x 0.7 = 0.42 OR Doesn’t Attend P(A,D) = 0.6 x 0.3 = 0.18 0.3 OR Attends P(D,A) = 0.4 x 0.7 = 0.28 0.7 0.4 Doesn’t Attend P(D,D) = 0.4 x 0.3 = 0.12 0.3

b) Find the probability that at least one is red a) Find the probability that both discs are the same colour THINK… When you have an AT LEAST ONE question where you must consider THREE of the FOUR combined probabiltiies.. What would be another way to get the same answer? a) P(same) = 𝟒 𝟗 + 𝟏 𝟗 = 𝟓 𝟗 b) P(at least one red)= 𝟒 𝟗 + 𝟐 𝟗 + 𝟐 𝟗 = 𝟖 𝟗 𝟔 𝟗 RED P(R,R) = 𝟔 𝟗 x 𝟔 𝟗 = 𝟒 𝟗 OR 𝟔 𝟗 RED 𝟑 𝟗 P(R,W) = 𝟔 𝟗 x 𝟑 𝟗 = 𝟐 𝟗 WHITE OR OR 𝟔 𝟗 P(W,R) = 𝟑 𝟗 x 𝟔 𝟗 = 𝟐 𝟗 RED 1 – P(W,W)= 1− 𝟏 𝟗 = 𝟗 𝟗 − 𝟏 𝟗 = 𝟖 𝟗 𝟑 𝟗 WHITE P(W,W) = 𝟑 𝟗 x 𝟑 𝟗 = 𝟏 𝟗 𝟑 𝟗 WHITE

P(N,N) = ? 𝟗 𝟓𝟎 P(only one piece) = 𝟔 𝟓𝟎 + 𝟐𝟏 𝟓𝟎 = 𝟐𝟕 𝟓𝟎 𝟕 𝟏𝟎 P(Y,Y) = 𝟐 𝟓 x 𝟕 𝟏𝟎 = 𝟏𝟒 𝟓𝟎 YES 𝟐 𝟓 YES 𝟑 𝟏𝟎 P(Y,N) = 𝟐 𝟓 x 𝟑 𝟏𝟎 = 𝟔 𝟓𝟎 NO OR 𝟕 𝟏𝟎 P(N,Y) = 𝟑 𝟓 x 𝟕 𝟏𝟎 = 𝟐𝟏 𝟓𝟎 YES 𝟑 𝟓 NO P(N,N) = 𝟑 𝟓 x 𝟑 𝟏𝟎 = 𝟗 𝟓𝟎 𝟑 𝟏𝟎 NO

We’re DONE …for this year Senior 3 Probability Senior 2 Probability Possibility Space Diagrams Probability Tree Diagrams Prepare your mini-whiteboards

If you throw two dice, what is the probability of getting a “double”? 6, 6 6, 5 6, 4 6, 3 6, 2 6, 1 6 5, 6 5, 5 5, 4 5, 3 5, 2 5, 1 5 4, 6 4, 5 4, 4 4, 3 4, 2 4, 1 4 3, 6 3, 5 3, 4 3, 3 3, 2 3, 1 3 2, 6 2, 5 2, 4 2, 3 2, 2 2, 1 2 1, 6 1, 5 1, 4 1, 3 1, 2 1, 1 1 Second Dice First Dice

If you throw two dice, what is the probability of getting a “double”? 6, 6 6, 5 6, 4 6, 3 6, 2 6, 1 6 5, 6 5, 5 5, 4 5, 3 5, 2 5, 1 5 4, 6 4, 5 4, 4 4, 3 4, 2 4, 1 4 3, 6 3, 5 3, 4 3, 3 3, 2 3, 1 3 2, 6 2, 5 2, 4 2, 3 2, 2 2, 1 2 1, 6 1, 5 1, 4 1, 3 1, 2 1, 1 1 Second Dice First Dice 6 out of the 36 possible outcomes are “doubles”, so the probability is 𝟔 𝟑𝟔 = 𝟏 𝟔

P(two different colours) = P(R,B) or P(B,R) = 𝟐 𝟗 + 𝟐 𝟗 = 𝟒 𝟗 Based on the following tree diagram what is the probability I pick 2 different colours? P(two different colours) = P(R,B) or P(B,R) = 𝟐 𝟗 + 𝟐 𝟗 = 𝟒 𝟗

The Watsons regard one boy and one girl as the ideal family The Watsons regard one boy and one girl as the ideal family. What is the chance of getting one boy and one girl in their planned family of two? First Child Second Child Combined G B P(G,G) = 0.5 x 0.5 = 0.25 0.5 G B 0.5 P(G,B) = 0.5 x 0.5 = 0.25 P(B,G) = 0.5 x 0.5 = 0.25 P(B,B) = 0.5 x 0.5 = 0.25 Total = 1.00 The probability of getting one of each is: P(G,B) + P(B,G) = 0.25 + 0.25 = 0.5

Use your table to find the probability of getting a score of 7 In a game, two fair spinners are spun and a score is found by adding the numbers obtained together. Use your table to find the probability of getting a score of 7 Find the probability of getting a score of 4 or less Spinner A b) 2 outcomes out of 16 give a score of 7 a) 1 2 3 4 2 3 4 5 3 4 5 6 Spinner B 4 5 6 7 c) 5 6 7 8 6 outcomes out of 16 give a score of 4 or less

Johnny has a 0. 4 chance of scoring from a free-kick and a 0 Johnny has a 0.4 chance of scoring from a free-kick and a 0.7 chance of scoring from a penalty Freekick Penalty Score P(scores both) Score Miss P(scores one) Score Miss Miss P(scores neither)

Probability Revision Worksheet for Friday Remember do it carefully, it will be assessed!