Answer:
a) 1/22
b) 3/44
c) 3/11.
Explanation:
a).
Prob(picking a blue first) = 5/12.
Prob(picking a yellow next) = 4/11 ( as it is without replacement)
Prob(purple next) = 3/10
Probability of picking these in this order = 5/12 * 4/11 * 3/10
= 1/22 (answer).
Note the probabilities are multiplied because the 3 events are independent.
b)
Prob(all the same colour) = Prob(All are blue) + Prob(all are yellow) + Prob ( All are purple)
Prob(All are blue) = 5/12 * 4/11 * 3/10 = 1/22
Prob(all are yellow) = 4/12 * 3/11 * 2/10 = 1/55
Prob(all purple) = 3/12 * 2/11 * 1 /10 = 1/220
So probability there are all the same colour = the sum of the above
= 3/44 (answer).
c) I take this to mean that all 3 are a different colour.
This will be the number of combinations of blue, yellow and purple possible which is 3! = 6.
So the answer is 6 * 1/22 = 3/11.