Newspaper question

Hi, I'm sorry if this forum already has a similar question, but I haven't had a chance to search(and if I did, I'm not sure what I could search for...)

I'm stuck on this question, and I get different results from my friends, but all of the methods kind of make sense.

On a Sunday, there is 70% chance he buys the Sunday Times newspaper (event T) and 35% chance he buys the News of the World newspaper(event N). Furthermore these events are not unrelated, for if he has already bought the times then he only buys the news of the world 20% of the time.

i ) On what proportion of Sundays does he buy both newspapers?


So, I wrote that
P(T)= 0.7
P(N)= 0.35
P(N|T)= 0.2
And then I used the formula
P(N|T) = [P(N (intersection) T]/ T , and re arranged it to find P(N intersection T), which ends up as 0.2 x 0.7, 0.14.
Is this correct?
Do I have to consider that he buys the News of the World and then the Times, in that order?

Thanks

Quote:

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Originally Posted by Danclansman

Hi, I'm sorry if this forum already has a similar question, but I haven't had a chance to search(and if I did, I'm not sure what I could search for...)

I'm stuck on this question, and I get different results from my friends, but all of the methods kind of make sense.

On a Sunday, there is 70% chance he buys the Sunday Times newspaper (event T) and 35% chance he buys the News of the World newspaper(event N). Furthermore these events are not unrelated, for if he has already bought the times then he only buys the news of the world 20% of the time.

i ) On what proportion of Sundays does he buy both newspapers?


So, I wrote that
P(T)= 0.7
P(N)= 0.35
P(N|T)= 0.2
And then I used the formula
P(N|T) = [P(N (intersection) T]/ T , and re arranged it to find P(N intersection T), which ends up as 0.2 x 0.7, 0.14.
Is this correct?
Do I have to consider that he buys the News of the World and then the Times, in that order?

Thanks

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If you draw a tree diagram you'll clearly see that your answer is correct.

The first two branches are T (0.7) and T' (0.3). The next two branches (that each go from T and T') are N and N'. The N branch from T has a probability 0.2. The N' branch from T has a probability of 0.8.

The N and N' branches from T' can be found from the fact that the total probability of N is 0.35. You will probbaly need to work this out for the later parts of the quesiton.

Ahhh I see now, thanks very much :)