Probability

True or False?

Answers

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

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

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.

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

DWhen two coins are tossed there are three possible outcomes: two heads, one head, or no heads. The probability of two heads is therefore

3

1 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

41

EThere are three outcomes in a football match: win, lose or draw.The probability of winning, if the teams are equally matched, is therefore

3

1

False, and I have tried to explain why...(next slide)

Suppose team A score 1 goal, and team B scores other possible numbers:

A, B1, 01, 11, 21, 31, 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

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.

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.

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.

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.

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.

Number of heads Probability

0 0.015625

1 0.093750

2 0.234375

3 0.312500

4 0.234375

5 0.093750

6 0.015625

The calculations are based on something called the Binomial Distribution

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.

LIt is harder to score a double than any other combination of dice.

True – see the next slide

Blue

Dice

1 2 3 4 5 6

1 1, 1 1, 2 1, 3 1, 4 1, 5 1, 6

2 2, 1 2, 2 2, 3 2, 4 2, 5 2, 6

Red 3 3, 1 3, 2 3, 3 3, 4 3, 5 3, 6

Dice

4 4, 1 4, 2 4, 3 4, 4 4, 5 4, 6

5 5, 1 5, 2 5, 3 5, 4 5, 5 5, 6

6 6, 1 6, 2 6, 3 6, 4 6, 5 6, 6

Imagine two separate dice, one red and one blue. The combinations are as follows:

Of the thirty six combinations, only six are doubles, which is not half of all possible results.

MComing into college I could be early, on time, or late. Therefore the probability of being late is 1/3.

False – see the next page.

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!

NThe 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