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## Instructions

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**Instructions**You will initially be given a set of questions of ‘Level 1’ difficulty. Once you’ve completed these questions, put your hand up, I’ll check your answers to see they’re mostly correct, then give you the next level up. You may work in pairs. Example Two boys apply to Tiffin. Bob has a 0.3 chance of getting in. Martin has a 0.4 chance of getting in. Calculate the probability that neither boy gets in. P(neither get in) = 0.7 x 0.6 = 0.42 Some questions require you to use the rules of independence and mutual exclusivity. Others might require you to think about the sample space.**Answer Sheet**Level 2 Level 1 Q1 Q1 Q2 Q2 Q3 Q3 Q4 Q4 Q5 Q5 Q6 Q7 Q6 Q7 Level 3 Q1 Q4 Q2 Q5 Q3 QN**Level 1**Q1 Q2 Q3 Q4 I pick a card from a pack at random, then put it back, then shuffle and pick another. What’s the probability I get 2 Kings? I have two dice and a pack of cards. What’s the probability that I roll two 6s and get a club? I toss two coins. What’s the probability I get exactly 1 Head? I toss two coins. What’s the probability I get two heads or two tails?**Level 1**Q5 Q6 Q7 I have a 30% probability of getting gold at IMC. My friend has a 60% chance. What’s the probability that I get gold but he doesn’t? I throw two dice. What’s the probability I get two 2s, two 3s or two 5s? I throw two dice. What’s the probability the sum is greater or equal to 10?**Level 2**Q1 Q2 Q3 Q4 Gladys has a 60% chance of getting a Distinction in Extreme Granny Surfing. Mildred has a 30% chance. What’s the probability that just one of them gets a Distinction? I roll two dice. What’s the probability I get a 1 and a 2? I have 3 yellow marbles, 2 green and 1 red. Dave picks a marble (without moving it). Max then picks one. What’s the probability that they pick the same colour? I pick a card without putting it back. Then John picks one from the same pack. What’s the probability we both get Kings?**Level 2**Q5 Q6 Q7 I have the letters ‘A’, ‘T’ and ‘C’ printed on 3 cards, and a monkey randomly arranges them in a line. What’s the probability it spells ‘CAT’? Now, I have 4 cards with the letters ‘C’, ‘A’, ‘H’ and ‘T’, and a French monkey. If it again randomly puts the letters in a line, what’s the probability I get the word ‘CHAT’? If I throw two dice, what’s the probability I get a 1 and 2, or a 3 and 4, or a 5 and a 6.**Level 3**Q1 Q2 Q3 Q4 Michael’s Ferrari has a 60% chance of breaking down this year. Tom’s Aston Martin has a 50% chance of breaking down. And Prannay’s BMW has a 40% chance. What’s the probability that exactly two cars break down? I toss 10 coins. What’s the probability that I get between 1 and 9 heads? I have 3 yellow marbles, 2 green and 1 red. Ian picks a marble and doesn’t put it back. Mark then picks one. What’s the probability that they pick the same colour now? Now a Finnish monkey arranges the letters ‘S’, ‘K’, ‘S’, ‘I’ and ‘A’ in a line. What’s the probability it spells the word KISSA?**Level 3**QN Q5 I’m capture by insane mathematicians and forced to play Russian roulette. I have a gun with n slots in the barrel and 1 bullet. I shoot, then if I survive, I rotate the barrel randomly then shoot again. I shoot n times. Give an expression for the probability of me surviving (in terms of n). I have two shuffled packs of cards on the table. I turn two cards over at time. If the two cards exactly match, I die immediately, unless they’re the last card of each pack. What’s the probability that I survive?**Answers**Level 1 Level 2 Q1 1/169 Q1 27/50 Q2 1/144 Q2 1/18 Q3 1/2 Q3 7/18 Q4 1/2 Q4 1/221 Q5 3/25 Q5 1/6 Q6 1/12 Q6 1/24 Q7 1/6 Q7 3/18 Level 3 Q1 19/50 Q4 1/60 Q2 1022/1024 Q5 (1-(1/n))n Q3 4/15 QN 1/52