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# Probability help watch

The question says that a bag has seven triangles, 3 blue and 4 red, and eleven squares of which 5 are blue and 6 are red. I have to pick two items at random and not replace. I've put this data into a table to answer the following:

1) Probability of same shape = 7/18*6/17 + 11/18*10/17 = 76/153

2) Probability of same colour = 8/18 * 7/17 + 10/18 * 9/17 = 73/153

All ok so far....

3) The final question is the probability of the same shape and same colour.

After trial and error I've got the right answer which is: 3/18*2/17 + 4/18*3/17 + 5/18*4/17 + 6/18+5/17 = 2/9

However, I don't understand why simply multiplying the answers to parts 1 and 2 doesn't give the right answer.

Many thanks
2. You can't use the formula P(A intersection B) = P(A) x P(B), because this is for independent events only. Instead you need P(A intersection B) = P(A) x P(B|A). I sometimes find calculating P(B|A) confusing or time consuming and that's when I draw a tree diagram (even if it's quite huge) and that ALWAYS help.
Try to draw the tree diagram and you'll see why the result is 2/9.
3. (Original post by ludmila)
You can't use the formula P(A intersection B) = P(A) x P(B), because this is for independent events only. Instead you need P(A intersection B) = P(A) x P(B|A). I sometimes find calculating P(B|A) confusing or time consuming and that's when I draw a tree diagram (even if it's quite huge) and that ALWAYS help.
Try to draw the tree diagram and you'll see why the result is 2/9.
Thank you ludmila - that's really helped!

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