Probability Name: Objectives: To know how to calculate the probability of an outcome not taking place. To be able to list all possible outcomes of two or more events in a systematic manner. Starter 1) What is the probability of the following outcomes? a) Throwing a 1 with a dice. b) Throwing a 6 with a dice. c) Tossing a coin and getting a tail. d) Throwing a 2 or a 6 with a dice. e) Throwing an even number with a dice. f) Throwing a prime number with a dice. 2) A ball contains blue balls and 2 red balls. Calculate the probability of: a) choosing a blue at random. b) choosing a red ball at random. c) choosing a black ball at random. d) choosing a blue or a red ball. 3) A bag contains 0 balls. 10 are green, 1 are red and the rest are white. Gemma takes a ball from the bag at random. What is the probability that she takes the following? a) a green ball: b) a white ball. c) a red ball. d) a ball that is not green or white. 4) In a school raffle, 200 tickets are sold. Dean has 0 tickets. What is the probability that he wins first prize?
) A pencil case contains six red pens and five blue pens. Geoff takes out a pen without looking. What is the probability that he chooses: a) a red pen? b) a blue pen? c) a red or a blue pen? d) add together the probabilities for parts (a) and (b). What do you notice? 6) The numbers 1 to 10 are placed in a hat. Chandni takes a number out of the bag without looking. What is the probability that he draws the following? a) the number 7. b) an even number. c) a number greater than 6. d) a number less than 3. e) a number between 2 and 8. 7) A bag contains 2 coloured balls. 12 are red, 7 are blue and the rest are green. Martin takes a ball at random from the bag. a) Find the following. i) P(he chooses red) ii) P(he chooses a blue) iii) P(he chooses a green) b) Add together the probabilities. What do you notice? 8) Think about the following: a) What is an event? b) What is an outcome? Probability that an outcome of an event will not happen 1) a) The probability of winning a prize in a raffle is 1. What is the probability of not 20 winning a prize in the raffle? b) The probability that it will rain tomorrow is 7, what is the probability that it doesn t 10 rain?
c) The probability of getting a tail from an unfair coin is 3. What is the probability of getting a head? d) The probability that Nicky will pass his driving test is 3. What is the probability of 7 him failing? 2) A set of 2 cards are shown. a) What is the probability of choosing a card with a sheep on it? b) What is the probability of choosing a card without a sheep on it? c) What is the probability of choosing a card with fish on it? d) What is the probability of choosing a card without a fish on it? 3) An unfair dice has the following probabilities: P(1) = 1 10 P(2) = 2 10 P(3) = 2 10 P(4) = 1 10 P() = 1 10 What is the probability of choosing a 6? 4) There are some blue, red, green and purple balls in a bag. A ball is chosen at random. Find P(purple) if these are the probabilities of the other outcomes: a) P(Blue) = 1 10 P(red) = 3 10 P(green) = 3 10 b) P(Blue) = 8 20 P(red) = 7 20 P(green) = 1 20 c) P(Blue) = 1 10 P(red) = 1 10 P(green) = 1 ) Jean is going on an activities holiday. Each activity lasts a whole day. She can only do one activity a day. The probability that she will go pony-trekking on any one day is 3. a) Work out the probability that Jean will not go pony-trekking on the first day. The probability that Jean will go windsurfing on any one day is 1. 10 b) Work out the probability that Jean will go windsurfing or pony-trekking on the first day. 6) The weather tomorrow will be sunny, cloudy or raining. If P(sunny) = 2, P(cloudy) = 1, what is P(raining)? 4 7) At break time, Chet has a choice of coffee, tea or hot chocolate. If P(he chooses coffee) = 1, 3 P(he chooses hot chocolate) = 1, what is P(he chooses tea)?
8) Amelia is either early, just in time or late for work. If P(late) = 3, what is 7 P(early or on time)? 9) In a cash bag there are three 1 pence coins, four 2 pence coins, six pence coins and two 10 pence coins. If a coin is drawn at random, what is the probability that the coin: a) is a 1p? b) is a copper coin? c) is not a p or 10p? d) is a 1p or p? e) is not a copper coin? f) is not a 1p, 2p or p Listing possible outcomes of an event 1) Two fair coins are thrown. Complete the table shown: From the list find the probability of getting: a) two heads. Coin 1 Coin 2 H H b) two tails. c) one of each. 2) John has 2 pairs of shoes, one black and the other brown. He has 3 pairs of socks, one black, one green and one red. a) List the different combinations of shoes and socks that John could wear. b) John gets dressed in the dark. Find the probability of him wearing: i) brown shoes and red socks. ii) black socks and shoes. iii) something black. 3) Chelsea flips a coin and throws a dice. a) List the possible outcomes that could take place. b) What is the probability that: i) she gets a head and a 1? ii) she doesn t get a tail and a? iii) she gets a head and an even number? iv) she doesn t get a head and an odd number?
4) Niall has a circular and triangular spinner numbered as shown. On each spinner it is equally likely to land on any of the numbers. Niall spins them both and gets a 1 followed by a. He writes it down like this: (1,). a) List all the possible outcomes he could get. b) If he adds the two scores together, find the probability that he: i) gets a score of 10. ii) gets a score greater than 12. iii) gets a score of 4. iv) doesn t get a score less than 13. ) Anne, Barry and Colin have booked three seats next to each other at the cinema. One possible way they could sit is shown here: a) Complete the table to show the possible ways they could sit. b) What is the probability that: i) Colin sits in the middle? ii) Anne does not sit in the middle? iii) Anne and Barry sit next to each other? Seat 1 Seat 2 Seat 3 A B C 6) Sajid and Kate go to the drinks machine. They buy a drink each. The drinks machine has Cola, Orange and Lemonade. a) List all the possible ways they could buy two drinks. b) it is equally likely as to which drinks they buy, find the probability that they: i) both get a cola. ii) buy one cola and one orange. iii) buy at least one cola. Challenge: 7) Joanne, Karen, Larry and Mick are travelling in the same car. The car has four seats. a) Complete the table showing all the possible ways they could be seated. (Hint, there are 24 possible coutcome) b) What is the probability that: i) Joanne is in the back? ii) Karen is in the front? iii) neither Karen and Larry are driving. Front Back Left Right (driver) Left Right J K L M
8) Anthony, Ben, Charlotte and Dianna are going to play in a mixed doubles tennis tournament. a) Write all the possible mixed pairs they could play in. b) Emily joins them. Write all the possible mixed pairs they could plan now. c) Fran decides that she wants to join in! Write down all the possible mixed pairs they could play now. d) Would you credit it, Georgia wants to play now! Write down all the possible mixed pairs they could play now. e) Try to find some sort of rule relating the number of combinations to the number of girls playing. Experiment Choose two of the following, two coins and one dice. List the possible outcomes in the appropriate table below. Flip one/two of your coins, and/or roll one of your dice, and repeat this 40 times, recording the number of times each outcome occurs. Coin 1 Coin 2 Number of successful outcomes Coin Dice
Dice 1 Dice 1 Plenary A) Two dice are thrown. Complete the following table to show the possible outcomes: Dice 2 1 2 3 4 6 1 (1,1) 2 3 4 6 What is the probability of getting: a) The same number on both dice? b) An even number on both dice? c) An even number on the first dice and any number on the second? d) A 3 on the first dice and not a on the second? B) The score on the dice are added together. Complete the following tables to show the possible scores and their probabilities. Dice 2 Outcome P(Outcome) 1 2 3 4 6 1 2 2 3 4 6 What is the probability of the outcome being: a) greater than 3? b) less than 7? c) less than 4 or greater than 6? C) If you finish, repeat part B but with the difference between the two numbers.