Question Working Answer Mark AO Notes Grade 1 a b c d e.g. There is a 0% chance of rolling a seven on a one to six fair die. It is impossible. There is a 99% chance that … There is a 75% chance that … There is a 50% chance that I will throw a head on a fair heads/tails coin. It is certain that I will throw one or the other. B1 B1 B1 B1 2 B1 for correct example B1 for correct example B1 for correct example B1 for correct example B 4 2 Example of a situation with equally likely outcomes with probability of , with justification. E.g. I have three counters in a bag. One red, one green and one blue. Each has the same chance of being drawn from the bag at random. There are three mutually exclusive outcomes. Each has the probability of of being drawn. B1 B1 2 B1 for correct example B1 for justification using example B 2 3 8 out of 10 3 out of 10 B1 B1 2 B1 for words equivalent to 80% oe B1 for words equivalent to 0.3 oe B 2 4 No The theoretical probability is predictive not exact. 10 is a limited number of experiments and will only sometimes produce five heads B1 B1 2 3 B1 for No. B1 for good explanation B 1
16 She should multiply the number of students (n) she has by the probability of being left-handed (0.14). The number of left-handed students will be 0.14n. B1 2 B1 for correct description of process M 1 17 P(E only) + P(E∩M) + P(M only) = 1 P(E∩M) = P(E only) = – = Therefore P(M) = 1 – P(E only) 1 – = P(Maths) = B1 M1 M1 A1 3 B1 for accuracy and use of Venn oe M1 for use of all probabilities sum to 1 oe M1 for calculation of fraction oe A1 cao M 4 18 The frequency is approximately the same for each region of the spinner, suggesting that the spinner is likely to be fair. There are no obvious anomalous results to indicate bias. So there is no strong evidence to suggest it is not fair. B1 2 M1 for explanation H 1 19 Joy wins: 0.65 × 52 = 33.8 which is approximately 34 wins Vicky won 10 times Joy + Vicky = 44 wins Max = 52-44 = 8 wins Max can expect to win 8 times. M1 A1 2 3 M1 for multiplication to find the number of Vicky’s wins A1 cao H 2
23 a b c 100 ÷ 36 = 2.7 P(1, 1) = He can expect to win one in 36 so should expect to have 36 goes to win at least once. If he has 100 goes, then he can expect 3 wins. M1 A1 B1 B1 3 M1 for good use of diagram such as two way table to support explanation A1 cao B1 for correct interpretation of 36 outcomes, of which only one wins B1 for division, rounding and correct interpretation in context H 4 24 P(BB) = × = P(RB) = 1 – (P(BB) + P(RR)) = 1 – ( + ) = as required. M1 A1 3 M1 for multiplication of × and subtraction from 1 A1 for use of technical notation and possible use of tree diagram to aid explanation H 2 25 a b P(PP) = 0.4 x 0.5 = 0.2 0.2 M1 B1 A1 3 M1 for correct construction of probability tree diagram B1 for probabilities and events identified clearly A1 cao H 3
26 P(6, 7, 8) = × = = 0.04977… 0.050 M1 A1 2 M1 for multiplication showing without replacement for two draws A1 cao H 2 27 a b c P(late) = 0.08 P(not late) = 0.92 P(early) = 0.02 P(not early) = 0.98 P(rain) = 0.3 P(not rain) = 0.7 P(on time) = 1 – P(late) – P(early) = 1 - 0.08 – 0.02 = 0.9 P(on time, not raining) = 0.9 × 0.7 = 0.63 P(rain, rain, rain)= 0.33 = 0.027 P(not late five days in a row) = 0.925 = 0.6591 0.63 0.027 0.659 B1 B1 B1 2 B1 for correct multiplication for different events oe B1 for correct multiplication for three same events oe B1 for correct multiplication for three same complement events oe H 3