Recall Date 19 February 2021 Title Wenn diagrams

Recall Date: 19 February 2021 Title: Wenn diagrams and probability = 1 48 2800 =8 Goal-Free • 70° and 40° or 55° and 55° = 4 000 9 n - 6 70° and 40° or 55° and 55°. Homework due:

Learning objectives: To use Venn diagrams to calculate probability.

Hook (same/different)

I do We do Students in a class are asked what sort of music (Classical or Rock) they like. The results are shown in this Venn diagram. Students in a class are asked what sort of music they like. The results are shown in this Venn diagram. Grime (G) (P) Pop C 15 R 5 10 5 How many students were in the class? 12 + 8 + 5 + 7 = 32 Students are then chosen at random. Calculate the following probabilities: i) P(pop) 15 + 10 + 5 = 35 Students are then chosen at random. Calculate the following probabilities: i) P(R)

Practice Races entered Frequency Road biking (R) only 53 Mountain biking (M) only 37 Both 17 ξ M R 53 17 13

Practice 2. Students in a year of 120 were asked what they do with their summer holiday. 71 students said they liked going on holiday and 66 students said that they like spending time with friends, 36 students said they liked both. a) Represent this information in a Venn diagram. b) Calculate the following probabilities:

Practice 3. Cam asks the 30 students in his class if they passed their Biology and Chemistry tests. 21 passed both. 2 didn’t pass either. 25 passed Chemistry. Draw a Venn diagram to show this information.

Mark

Practice Races entered Frequency Road biking (R) only 53 Mountain biking (M) only 37 Both 17 1. a) ξ M R 53 17 37 13

Practice 2. Students in a year of 120 were asked what 2. a) they do with their summer holiday. 71 students said they liked going on holiday and 66 students said that they like spending time with friends, 36 students said they liked both. F H 35 30 36 a) Represent this information in a Venn diagram. b) Calculate the following probabilities: 19 b)

Practice 3. a) 3. Cam asks the 30 students in his class if they passed their Biology and Chemistry tests. 21 passed both. 2 didn’t pass either. 25 passed Chemistry. C B 4 3 21 2 a) Draw a Venn diagram to show this information.

Name: ξ = {230 students in a school} 147 students take French (F). 94 students take Spanish (S). 15 students do not take French or Spanish. . . 1. (a)Complete the Venn diagram. [3 marks] 121 26 68 15 2. (b)A student is chosen at random. Work out the probability that the student takes Spanish but not French. [1 mark] 2 (c) Work out P(F U S) Mastery Matrix C 13. 3 I can construct Venn diagrams and two-way tables to solve probability problems [1 mark] 0 -2 3 4 -5 Mastery Matrix C 13. 3 I can construct Venn diagrams and two-way tables to solve probability problems 0 -2 3 4 -5

FOUNDATION: Hegarty. com Clip numbers: 383 and 391

“ mutually exclusive events” Which of these events cannot happen at the same time? a) The weather being sunny and raining Yes b) Rolling an even number and a number less that Yes 3 on a dice c) Picking a card out of a deck that is black and a heart No d) Rolling an even number and an odd number on a six sided dice No

Getting a odd number and an even number at the same time are mutually exclusive. 1. The sum of the probabilities of all the mutually exclusive events is 1. 2. When two events, A and B, are mutually exclusive: P(A or B) = P(A) + P(B) This is called the addition law or “OR” rule

Outcome 1 2 3 Probability 0. 1 0. 4 0. 1 4 Work out P(4 or 5). P(4) = 1 – (0. 1 + 0. 4 + 0. 1 + 0. 25) = 0. 15 P(4 or 5) = P(4) + P(5) = 0. 15 + 0. 2 = 0. 35 5 6 0. 2 0. 05 Outcome 1 2 Probability 0. 1 0. 25 3 4 5 6 0. 05 0. 2 0. 15 Work out P(3 or 5). P(3) = 1 – (0. 1 + 0. 25 + 0. 05 + 0. 2 + 0. 15) = 0. 25 P(3 or 5) = P(3) + P(5) = 0. 25 + 0. 2 = 0. 55

Colour Red Green Probability 0. 4 0. 3 Yellow Black Colour Red Green Yellow Black Probability 0. 4 0. 3 0. 2 0. 1 P(G or Y) = P(G) + P(Y) = 0. 3 + 0. 2 = 0. 5 1. A bag contains only red, green, yellow and black marbles. Calculate P(G or Y) Colour Red Green Yellow Black x 2 x 4 x x Colour Red Green Yellow Black Probability x 2 x 4 x x 2. A bag contains only red, green, yellow and black marbles. The probability of picking a red and black marble is the same. a) Calculate P(R), give your answer as a fraction. b) Calculate P(R or Y), give your answer as a fraction. Colour Probability Red Green Yellow 2 x 8 x Black 3. A bag contains only red, green, yellow and black marbles. The probability of picking a yellow marble is twice that of picking a black marble. You are half as likely to pick a red marble than a green marble. Calculate P(R or B), give your answer as a fraction. Colour Red Green Yellow Black Probability x 2 x 8 x 4 x

Higher: hegarty. com Clip numbers: 380 - 391