Probability True or False? Answers
A When 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
B Scoring a total of three with two dice is twice as likely as scoring a total of two. True – look at the combinations: next slide
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.
C In 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
D When two coins are tossed there are three possible outcomes: two heads, one head, or no heads. The probability of two heads is therefore False – look at the combinations: next slide
False because there are four outcomes: HH, HT, TH, TT So the probability of HH is one out of four, or
E There are three outcomes in a football match: win, lose or draw. The probability of winning, if the teams are equally matched, is therefore False, and I have tried to explain why. . . (next slide)
Suppose team A score 1 goal, and team B scores other possible numbers: A, B 1, 0 1, 1 1, 2 1, 3 1, 4 etc Only 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
F In 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.
G After 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.
H In 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.
I My 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.
J The probability of getting exactly three heads when I toss a coin six times is ½. False – and there a large number of possible outcomes. The actual probabilities are shown on the next page.
Number of heads The calculations are based on something called the Binomial Distribution Probability 0 0. 015625 1 0. 093750 2 0. 234375 3 0. 312500 4 0. 234375 5 0. 093750 6 0. 015625
K There 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.
L It is harder to score a double than any other combination of dice. True – see the next slide
Imagine two separate dice, one red and one blue. The combinations are as follows: Red Dice 1 2 3 4 5 6 1 1, 1 2, 1 3, 1 4, 1 5, 1 6, 1 2 1, 2 2, 2 3, 2 4, 2 5, 2 6, 2 Blue 3 1, 3 2, 3 3, 3 4, 3 5, 3 6, 3 Dice 4 1, 4 2, 4 3, 4 4, 4 5, 4 6, 4 5 1, 5 2, 5 3, 5 4, 5 5, 5 6, 5 Of the thirty six combinations, only six are doubles, which is not half of all possible results. 6 1, 6 2, 6 3, 6 4, 6 5, 6 6, 6
False – see the next page. M Coming into college I could be early, on time, or late. Therefore the probability of being late is 1/3.
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!
N The probability of there being an eclipse at noon tomorrow is zero. True – again, look at the records.
O If 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.
How did you fare? Colin
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