Question

A bag contains 4 red, 3 yellow and 2 purple discs. A disc is taken, at random, from the bag and is not replaced. A second disc is then taken, at random, from the bag. Calculate the probability that the two discs taken from the bag are different colours?

please help

Answer 1

`Pr=13/18`

Explanation:

The first thing to do is to convert these possibilities into a tree diagram, like the one below which I did in Word:

Where `R` equals red disc, `Y` equals yellow disc and `P` equals purple disc.

To find the probability of 2 discs being chosen that are different colours, we simply subtract the probabilities that both colours are the same from 1. This means we must find `Pr (R,R), (Y,Y) and (P,P)`.

From the diagram, we see
`Pr (R,R) = 4/9 *3/8`
`Pr (R,R) = 12/72 = 1/6`.
We also see
`Pr (Y,Y) = 3/9*2/8`
`Pr (Y,Y) = 6/72 = 1/12`
and
`Pr (P,P) = 2/9 * 1/8`
`Pr (P,P) = 2/72 = 1/36`.
Next we add all these probabilites together to get
`1/6 + 1/12 + 1/36 = 5/18.`

Since the probabilities of getting the same colour are complementary to getting different colours, we can use the rule
`Pr(A')= 1 - Pr(A)`, where `A'` is the complementary group of `A`.
https://www.ck12.org/probability/complement-rule-for-probability/lesson/Complement-Rule-for-Probability-ADV-PST/

Therefore,
`1- 5/18 = 13/18`, the probability of getting different coloured disks.

I hope I helped!