# Math Help - Using tree diagrams

1. ## 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?

Thankyou

2. Originally Posted by Nat077
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?

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.

3. Originally Posted by Nat077
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?

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

Originally Posted by janvdl
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: $\left( \frac{4}{5} \right)\, \left( \frac{4}{7} \right) + \left( \frac{1}{5} \right)\, \left( \frac{3}{7} \right) = \frac{19}{35}$.