# Using tree diagrams

• Mar 22nd 2008, 06:19 AM
Nat077
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
• Mar 22nd 2008, 07:01 AM
janvdl
Quote:

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.
• Mar 23rd 2008, 03:35 AM
mr fantastic
Quote:

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.

Quote:

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