Mathematics Higher Level Robert Joinson

©Sumbooks2002Higher Level79. Relative Probability1. A biased coin is tossed 50 times. The number of times it comes down heads is 31 and thenumber of times it comes down tails is 19. If it is now tossed 1000 times, how many timeswould you expect it to show heads?2. In an opinion poll for the general election, 500 people in a constituency were asked whatparty they would vote for. 220 said they would vote for the Left party, 170 for the Rightparty and 110 for the Centre party. The 500 people can be taken as representative of thepopulation of the constituency.a) What is the probability that a person chosen at random will vote for:(i) the Left party (ii) the Right party (iii) the Centre party?b) It is expected that 45,000 people will vote in the election. Estimate the number of peoplewho vote for each party.3. A chocolate company make sugar coated chocolate sweets in red, yellow and green. It isknown that more people prefer red sweets than any other colour so the company mix themin the ratio 5 red to 3 yellow to 2 green.a) In a bag of 50 sweets, how many of each colour would you expect?b) David takes a sweet from the bag without looking at it. What is the probability that it willbe:(i) red (ii) yellow (iii) green?Sarah only likes the red sweets. She eats them all from her bag without eating any of theothers. She gives the bag to David who now takes a sweet. What is the probability that it is:(i) green (ii) yellow?During one days production of sweets at the factory, the company make 100,000 greensweets. How many red and yellow sweets do they make?4. An unfair triangular spinner has the numbers 1, 2 and 3 on it. It is spun 100 times. Number1 is obtained 25 times, number 2 occurs 30 times and number 3 occurs 45 times.a) Write down the probability of each number occurring.b) If it is spun 550 times, how often would you expect each number to occur?5. A survey is carried out over a period of six days to determine whether the voters are for oragainst having a new by-pass outside their town. Each day 50 people were asked theiropinion. The results were put into the following table.Number of people 50 100 150 200 250 300Number ‘for’ 30 45 55 83 96 122Number ‘against’ 20 55Probability ‘for’ 0.60 0.45Probability ‘against’ 0.40 0.55a) Copy and complete the table.b) On graph paper plot ‘Number of people’ against ‘Probability for’. Use a scale of 2cm torepresent 40 people on the horizontal axis and 2cm to represent 0.1 on the vertical axis.c) From your graph estimate the probability that a voter chosen at random would be for theby-pass.d) There are 70,000 voters in the town. If the people asked were a representative sample ofthe voting population, how many would you expect to be against the by-pass?