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ntrik
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11) A boy always either walks to school or goes by bus. If one day he goes to school by bus, then the probablity that he goes by bus the next day is 7/10. If one day he walks to school, then the probablity that he goes by bus the next day 2/5.

a) Given that he walks to school on a particular Tuesday, draw a tree diagram and hence find the probablity that he will go to school by bus on Thursday of that week.

b) Given that the boy walks to school on both Tuesday and Thursday of that week, find the probablity that he will also walk to school on Wednesday. (You may assume that the boy will not be absent from school on Wednesday or Thursday of that week.)

Can anyone help? This stuff does my head in.
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the_anomaly
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Do you know what the answers are meant to be? I will probably be able to work it out if I know the answers.
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ntrik
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Sure.

a) 11/23
b) 3/4

I think those are the answers anyway. It just says in the back "11) 13/23, 3/4"
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the_anomaly
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Sorry the scan quality is so bad - had to reduce the resolution to keep the file size down. Anyway, hope this helps.
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ntrik
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Whoa, thanks for that.
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ntrik
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Ok here we go again. Another probability question anyone would like to attempt it.

11) Seven identical balls are marked respectively with the numbers 1 to 7 inclusive. The number on each ball represents the score for the ball. The seven balls are then put into a bag. If 2 balls are chosen at random one after the other, find the probability of obtaining a total score of 11 or more:

a) if the first ball is replaced
b) if the first ball is not replaced.
If 2 balls are chosen at random one after the other from 7 balls find, in case (a) and in case (b), the most probable total score for the 2 balls with its associated probability.

I can do part (a) where I drew a grid representing all possible outcomes but for part (b) what do I do?
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the_anomaly
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(Original post by ntrik)
Ok here we go again. Another probability question anyone would like to attempt it.

11) Seven identical balls are marked respectively with the numbers 1 to 7 inclusive. The number on each ball represents the score for the ball. The seven balls are then put into a bag. If 2 balls are chosen at random one after the other, find the probability of obtaining a total score of 11 or more:

a) if the first ball is replaced
b) if the first ball is not replaced.
If 2 balls are chosen at random one after the other from 7 balls find, in case (a) and in case (b), the most probable total score for the 2 balls with its associated probability.

I can do part (a) where I drew a grid representing all possible outcomes but for part (b) what do I do?
You need to determine how many outcomes there are that give a score greater than 11, remembering the balls are not replaced, so you cannot have an outcome such as 1st ball 6, and 2nd ball 6.

Therefore the outcomes are:

4,7
5,6
5,7
6,5
6,7
7,4
7,5
7,6

i.e. there are 8 outcomes. If you consider a tree diagram, the probability would be:

1/7 x 1/6 x 8

As when the first ball is selected you are selecting one from 7, but the next time you have already picked a ball out, so there are only 6 remaining balls left.

So the probability is 4/21

Next, the most probable score in case (a): This is obviously going to be the score for which there are the greatest number of combinations to attain that score. The best way to see this is to complete a sample space diagram (a grid representing all possible outcomes). You will realise that the most probable score is 8 as there are 7 ways to make this score. To work out the probability you consider a tree diagram remembering the probabilities are unconditional. So the probability will be:

1/7 x 1/7 x 7 possible ways of making the score = 1/7

A similar approch can be used for determining the most probable score in case (b) but remembering that you cannot have the same number on the second ball as you are not replacing the balls. You will find that there are an equal number of ways (6 ways) to makes scores of 7,8, and 9. By again considering a tree diagram, the probability will be

1/7 x 1/6 x 6 = 1/7

Hope this helps
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ntrik
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Thanks a lot. I appreciate it.
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