Why do they bother with probability questions

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Zenarthra
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For ai) why can't I multiply the probability of A' and E' are the events not independent?
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SherlockHolmes
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(Original post by Zenarthra)
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For ai) why can't I multiply the probability of A' and E' are the events not independent?
P(A n B) does not equal P(A)P(B) so the events are not independent.
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Zenarthra
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(Original post by SherlockHolmes)
P(A n B) does not equal P(A)P(B) so the events are not independent.
Yeah o figured thanks, for tree diagrams are they only for independent events?
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SherlockHolmes
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(Original post by Zenarthra)
Yeah o figured thanks, for tree diagrams are they only for independent events?
No I don't think so. You could use it for this example if you wanted. Just be careful with your probabilities. The table is probably the safest method for this question though.
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Zenarthra
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(Original post by SherlockHolmes)
No I don't think so. You could use it for this example if you wanted. Just be careful with your probabilities. The table is probably the safest method for this question though.
Have I set up this tree diagram correctly?
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Can't seem to get even part a correct?
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TeeEm
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Why do they bother with probability questions?
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SherlockHolmes
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(Original post by Zenarthra)
Have I set up this tree diagram correctly?
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Can't seem to get even part a correct?
Not quite. The probabilities in the second tier of your tree are incorrect. I suppose I should say that although a tree diagram will be able to show all the probabilities, it is typically used for events with two outcomes that can be simulated more than once like tossing a coin. So the probabilities in the next tier of the tree are conditional probabilities. In this example the outcomes of A and E happen at the same time so it wouldn't really make sense to have conditional probabilities.

So if we just use the tree so that we can see the probabilities and forget about the above, the first probability in the second tier of your tree shouldn't be 0.6. It should be P(E|A). P(E|A) = P(A n E)/P(A) = 0.55/0.85.

If you don't understand the above, it is probably best to leave it. I would definitely use the table for questions like these anyway.
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Zenarthra
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(Original post by SherlockHolmes)
Not quite. The probabilities in the second tier of your tree are incorrect. I suppose I should say that although a tree diagram will be able to show all the probabilities, it is typically used for events with two outcomes that can be simulated more than once like tossing a coin. So the probabilities in the next tier of the tree are conditional probabilities. In this example the outcomes of A and E happen at the same time so it wouldn't really make sense to have conditional probabilities.

So if we just use the tree so that we can see the probabilities and forget about the above, the first probability in the second tier of your tree shouldn't be 0.6. It should be P(E|A). P(E|A) = P(A n E)/P(A) = 0.55/0.85.

If you don't understand the above, it is probably best to leave it. I would definitely use the table for questions like these anyway.
No I understand it perfectly, thanks a lot that really helped!
The reason why I'm asking all these questions is because I don't have a teacher.
Thanks for answering 😃
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Zenarthra
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#9
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(Original post by SherlockHolmes)
Not quite. The probabilities in the second tier of your tree are incorrect. I suppose I should say that although a tree diagram will be able to show all the probabilities, it is typically used for events with two outcomes that can be simulated more than once like tossing a coin. So the probabilities in the next tier of the tree are conditional probabilities. In this example the outcomes of A and E happen at the same time so it wouldn't really make sense to have conditional probabilities.

So if we just use the tree so that we can see the probabilities and forget about the above, the first probability in the second tier of your tree shouldn't be 0.6. It should be P(E|A). P(E|A) = P(A n E)/P(A) = 0.55/0.85.

If you don't understand the above, it is probably best to leave it. I would definitely use the table for questions like these anyway.
I have a question, tossing a coin for a tree diagram isn't conditional probability is it?
Probability of tossing heads and tails remain constant through the tiers?
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Zenarthra
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#10
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(Original post by TeeEm)
Why do they bother with probability questions?
i think you mixed me up with the examiner.
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SherlockHolmes
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(Original post by Zenarthra)
I have a question, tossing a coin for a tree diagram isn't conditional probability is it?
Probability of tossing heads and tails remain constant through the tiers?
It is conditional. Let A be the event of the first coin toss landing heads. Let B be the event of the second coin toss landing heads. Then,

 P(A)=0.5 and P(B|A)=\frac{P(AnB)}{P(A)}=\frac{P(A)P(B)}{P(A)}=P(B)=0.5
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