# More-Likely-Than-Probable

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More-Likely-Than-Probable

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11/28/2009
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```							More Likely Than Probable
Each of the following statements talks about the chances of somethig hppening. Some are true, some are false and some require a bit of discussion. Look at each statement and say whether it is true or false. Explain and justify your answer using logic and the mathematics of probability.

Statements
A There are 13 people in a rugby league team, so it is certain that in any team there will always be two players who have their birthday in the same month. When two coins are tossed, the probability of getting one head and one tail is 1/2. In many board games you have to throw a 6 before you can start. They always ask for this because a 6 is the hardest number to get when you throw a dice. A fair way of choosing a number from 0-9 is to open a book at random and to take the units digit of the right-hand page number. When you throw a fair six-sided dice you are unlikely to get a prime number. If Kidderminster Harriers play Manchester United in a football match, they can win, draw or lose. So the probability that the Harriers will win must be 1/3. Bob says that he likes multiple choice questions because he is bound to get half of them right just by guessing. When you throw a six-sided dice it is harder to get a 6 than a 3 I have just tossed a fair coin nine times and it showed a head each time. If I now toss it a tenth time, it is more likely to show a tail than a head. A fair sided dice with faces numbered 1-10 is thrown twice. The number you get on the second throw will depend upon which number turned up on the first throw. On the next school sports day it is more likely to rain than not rain. I am more likely to win a raffle if I choose two raffle tickets from different places in the book than if I choose two consecutive tickets. Whenever I drop a piece of buttered toast, it always lands butter-side down If I drop a drawing pin, it can land either point up or point down. So the probability of landing point up is 1/2. If I blow on a dice before I throw it, I am more likely to get a six In the National Lottery, the set of six randomly distributed numbers 2, 23, 25, 34, 40, 44 is more likely to come up than the set of consecutive counting numbers 1, 2, 3, 4, 5, 6 In any rugby match there is a better than even chance that two of the players will have the same birthday

B

C

D

E F

G H I

J

K L

M N

O P

Q

answers A There are 13 people in a rugby league team, so it is certain that in any team there will always be two players who have their birthday in the same month. True. If each of twelve players have a birthday on different months of the year, then the thirteenth play must have his birthday in the same month as one of the other twelve.

B

When two coins are tossed, the probability of getting one head and one tail is 1/ . 2 True. HH HT TH TT

C

In many board games you have to throw a 6 before you can start. They always ask for this because a 6 is the hardest number to get when you throw a dice. False. Each of the six numbers have an equally likely chance of selection.

D

A fair way of choosing a number from 0-9 is to open a book at random and to take the units digit of the right-hand page number. False. If you look only at the right-hand page, you will only pick from the set of odd (or even) numbers. Also the total number of pages will not start at zero or end with a multiple of 9. Also there may be a title page, blank pages, contents pages and an index.

E

When you throw a fair six-sided dice you are unlikely to get a prime number. False. There are three prime numbers 2, 3 and 5 out of a total of six numbers.

F

If Kidderminster Harriers play Manchester United in a football match, they can win, draw or lose. So the probability that the Harriers will win must be 1/3. False. The probabilities of win, draw or lose are not equally likely

G

Bob says that he likes multiple choice questions because he is bound to get half of them right just by guessing. False. There are likely to be more than two options. Also, incorrect answers might be negatively marked to stop candidates guessing.

H

When you throw a six-sided dice, it is harder to get a 6 than a 3 False. Each of the six numbers have an equally likely chance of selection.

I

I have just tossed a fair coin nine times and it showed a head each time. now toss it a tenth time, it is more likely to show a tail than a head. False. Each toss of a coin is an independent event and is therefore not affected by the outcome of the previous event.

If I

J

A fair sided dice with faces numbered 1-10 is thrown twice. The number you get on the second throw will depend upon which number turned up on the first throw. False. Each throw of the dice is an independent event and is therefore not affected by the outcome of the previous event.

K

On the next school sports day it is more likely to rain than not rain. False. Surprisingly, there are fewer days when it rains than with no rain. You just remember the rainy days because you get wet!

L

I am more likely to win a raffle if I choose two raffle tickets from different places in the book than if I choose two consecutive tickets. False. Each number has an equally likely chance of selection

M

Whenever I drop a piece of buttered toast, it always lands butter-side down Maybe. The butter adds weight to one side and will therefore affect the areodynamics of the fall

N

If I drop a drawing pin, it can land either point up or point down. probability of landing point up is 1/2.

So the

False. The weight of the pin is not evenly distributed so it will affect the way that the pin lands. You can do an experiment by dropping a pin lots of times and recortding the result in a frequency table. O If I blow on a dice before I throw it, I am more likely to get a six. False. Each of the six numbers have an equally likely chance of selection and blowing on them will not make any difference (unless blowing on the dice makes the dice sticky!) P In the National Lottery, the set of six randomly distributed numbers 2, 23, 25, 34, 40, 44 is more likely to come up than the set of consecutive counting numbers 1, 2, 3, 4, 5, 6 False. Each of the 49 numbers has an equally likely chance of selection Q In any rugby match there is a better than even chance that two of the players will have the same birthday True. The chances of the second player not having the same birthday as the first is 364/365 The chances of the third player not having the same birthday as the first player or the second player is 364/365 times 363/365 The calculation for the whole team not sharing the same birthday is = 364/365 x 363/365 x 362/365 x 361/365 x 360/365 x . . . x 336/365 = 0.29 So the chances of two people (or more) sharing the same birthday is 0.71 which is better than even chance.

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