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Math Help - Using tree diagrams

  1. #1
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    Exclamation Using tree diagrams

    There are two fish tanks in a pet shop.
    In tank A there are four white fish and one black fish.
    In tank B there are three white fish and four black fish.
    One fish is to be taken out of tank A at random.
    One fish is to be taken out of tank B at random.

    Using a tree diagram, or otherwise, calculate the probability that

    (a) the two fish will both be white
    (b) the two fish will be of different colours


    Do you think i should give my answer in decimals or fractions?
    What answers did you get?

    Thankyou
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  2. #2
    Bar0n janvdl's Avatar
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    Quote Originally Posted by Nat077 View Post
    There are two fish tanks in a pet shop.
    In tank A there are four white fish and one black fish.
    In tank B there are three white fish and four black fish.
    One fish is to be taken out of tank A at random.
    One fish is to be taken out of tank B at random.

    Using a tree diagram, or otherwise, calculate the probability that

    (a) the two fish will both be white
    (b) the two fish will be of different colours


    Do you think i should give my answer in decimals or fractions?
    What answers did you get?

    Thankyou
    a) The probabilities are disjoint.

    Taking a white fish out of Tank A: 4/5
    Taking a white fish out of Tank B: 3/7

    Multiply them together.

    Probability is: 12/35

    ---------------------------

    b) I'm not sure about this one. I would work out the probability that they are of the same colour and then find the complement.
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  3. #3
    Flow Master
    mr fantastic's Avatar
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    Quote Originally Posted by Nat077 View Post
    There are two fish tanks in a pet shop.
    In tank A there are four white fish and one black fish.
    In tank B there are three white fish and four black fish.
    One fish is to be taken out of tank A at random.
    One fish is to be taken out of tank B at random.

    Using a tree diagram, or otherwise, calculate the probability that

    (a) the two fish will both be white
    (b) the two fish will be of different colours


    Do you think i should give my answer in decimals or fractions?
    What answers did you get?

    Thankyou
    Exact answers should be given and clearly that's easily done using fractions.

    Quote Originally Posted by janvdl View Post
    a) The probabilities are disjoint.

    Taking a white fish out of Tank A: 4/5
    Taking a white fish out of Tank B: 3/7

    Multiply them together.

    Probability is: 12/35

    ---------------------------

    b) I'm not sure about this one. I would work out the probability that they are of the same colour and then find the complement.
    I agree with the answer to (a).

    For (b), you'd use the tree diagram: \left( \frac{4}{5} \right)\, \left( \frac{4}{7} \right) + \left( \frac{1}{5} \right)\, \left( \frac{3}{7} \right) = \frac{19}{35}.
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