129 261 65 455 Male 101 69 25 Female 195 Total 230 330 90 650 April 2017 An MP is chosen at random from the 650 MPs. Explain why the events MP is and “the male” MP belongs to the Labour are not independent. “the Party” 7. In a school class, half the pupils represent the school at a winter sport, one third represent the school at a summer sport and one tenth do both. A student is chosen at random from this class. Find the probability that they represent the school at sport. 8.* The probability that a person is left-handed is 0.08. 91% of left-handers and 1% of are left-footed. What is the probability that a person chosen at random catches a ball with one hand but kicks it with the opposite foot? 9. Idris works five days a week, Monday to Friday. 0.3. The chance that he gets up late on any working day is Last week, Idris got up late exactly once during the working week. What percentage of working weeks would you expect this to happen? 10.* Ava has three cards. One card has both sides red, one has both sides black, and one has one red side and one black side. Ava holds up a random card with a random side facing you. The side you see is red. What is the probability that the other side of the same card is red? Extension 1, 4 3 In a game, three counters marked and are placed in a bag. Tom draws a counter from the bag at random, records the number and then replaces the counter in the bag. He repeats this until 5 5. the numbers he has drawn sum to or more. Tom wins if the numbers have a sum of exactly If 5, the sum is more than he loses. List all the possible winning combinations of numbers that Tom could draw, and all the possible 1, 3) 1, 1, 3) losing ones. For example, (1, would win but (1, would lose. Worked solutions 1. and 2. Because and are independent, A B A C). 3. This is the probability of given (B and C) C) A The probability of (B and is . The proportion of (B and that is also is then , or 4. This can be answered using a Venn diagram:
Male 129 261 65 455 Female 101 69 25 195 Total 230 330 90 650 April 2017 An MP is chosen at random from the 650 MPs. Explain why the events “the MP is male” and “the MP belongs to the Labour Party” are not independent. 7. In a school class, half the pupils represent the school at a winter sport, one third represent the school at a summer sport and one tenth do both. A student is chosen at random from this class. Find the probability that they represent the school at sport. 8.* The probability that a person is left-handed is 0.08. 91% of left-handers and 1% of are left-footed. What is the probability that a person chosen at random catches a ball with one hand but kicks it with the opposite foot? 9. Idris works five days a week, Monday to Friday. The chance that he gets up late on any working day is 0.3. Last week, Idris got up late exactly once during the working week. What percentage of working weeks would you expect this to happen? 10.* Ava has three cards. One card has both sides red, one has both sides black, and one has one red side and one black side. Ava holds up a random card with a random side facing you. The side you see is red. What is the probability that the other side of the same card is red? Extension In a game, three counters marked 1, 4 and 3 are placed in a bag. Tom draws a counter from the bag at random, records the number and then replaces the counter in the bag. He repeats this until the numbers he has drawn sum to 5 or more. Tom wins if the numbers have a sum of exactly 5. If the sum is more than 5, he loses. List all the possible winning combinations of numbers that Tom could draw, and all the possible losing ones. For example, (1, 1, 3) would win but (1, 1, 1, 3) would lose. Worked solutions 1. and 2. Because A and B are independent, 3. This is the probability of A given (B and C). The probability of (B and C) is . The proportion of (B and C) that is also A is then , or 4. This can be answered using a Venn diagram:
417253-section-check-in-statistics-probability.docx