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?

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1 Answer
Solace M.
Sep 29, 2017

#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:
enter image source here
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!

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