2 AWhen you roll a fair six- sided dice, it is harder to roll a six than a four.False – a fair dice, so all numbers have equal chance
3 BScoring a total of three with two dice is twice as likely as scoring a total of two.True – look at the combinations:next slide
4 True – look at the combinations: A score of two can only be obtained in one way – a 1 on each dice.A score of three can be obtained in two ways – 1 and 2 or 2 and 1, so the three is twice as likely.
5 CIn a lottery, the six numbers 3, 12, 26, 37, 44, 45 are more likely to come up than the six numbers 1,2,3,4,5,6.False – each number has the same chance
6 The probability of two heads is therefore When two coins are tossed there are three possible outcomes: two heads, one head, or no heads.The probability of two heads is thereforeFalse – look at the combinations:next slide
7 False because there are four outcomes: HH, HT, TH, TTSo the probability of HH is one out of four, or
8 There are three outcomes in a football match: win, lose or draw. The probability of winning, if the teams are equally matched, is thereforeFalse, and I have tried to explain why...(next slide)
9 Suppose team A score 1 goal, and team B scores other possible numbers: A, B1, 01, 11, 21, 31, 4 etcOnly one of these results is a draw, the rest are all win or lose, so the draw is least likely. Check some football scores on a Saturday, it is FALSE
10 FIn a ‘true or false’ quiz with ten questions, you are certain to get five right if you just guess.False – you would expect five right, but because of chance it won’t happen every time.
11 GAfter tossing a coin and getting a head five times in a row, the next toss is more likely to be a tail than a head.False – only gamblers believe their luck will change. The probability will be 1/2 each time, whatever happened before.
12 HIn a group of ten people the probability of two people being born on the same day of the week is 1.True. There are only seven days in a week, so some pair must have been born on the same day.
13 IMy friend has four daughters. If she has another baby, it is more likely to be a girl than a boy.False, same as with the coin, unless you look at scientific results, which might suggest various things.
14 JThe probability of getting exactly three heads when I toss a coin six times is ½.False – and there are a large number of possible outcomes.The actual probabilities are shown on the next page.
15 Number of headsProbability123456The calculations are based on something called the Binomial Distribution
16 There is an evens chance of it raining on any given day. KThere is an evens chance of it raining on any given day.False – just look at any weather records. It really does not rain on half the days of a year.
17 It is harder to score a double than any other combination of dice. True – see the next slide
18 Imagine two separate dice, one red and one blue Imagine two separate dice, one red and one blue. The combinations are as follows:BlueDice1234561, 11, 21, 31, 41, 51, 62, 12, 22, 32, 42, 52, 6Red3, 13, 23, 33, 43, 53, 64, 14, 24, 34, 44, 54, 65, 15, 25, 35, 45, 55, 66, 16, 26, 36, 46, 56, 6Of the thirty six combinations, only six are doubles, which is not half of all possible results.
19 False – see the next page. MComing into college I could be early, on time, or late. Therefore the probability of being late is 1/3.
20 Look at past records. I haven’t been late this year, so the probability is zero. Actually, over a college year, there is a small probability that I just might be late!
21 The probability of there being an eclipse at noon tomorrow is zero. True – again, look at the records.
22 OIf I play the national lottery, I have just as much chance of winning as anyone else.False – some people may buy lots more tickets than you.