Probability of Events.

Question

Adam is given a bag of 20 sweets of which 6 are strawberry flavoured, 6 are lemon flavoured and 8 are orange flavoured. Adam take out 5 sweets at random and eats them. Find the probability that he eats:

 

(a) 3 strawberry flavoured and 2 lemons flavoured

(b) exactly 2 strawberry flavoured sweets

(c) no lemon flavoured sweets

Is it any differences in answer if the events Adam picking 5 sweets simultaneously versus Adam picking 5 sweets one at a time?

Answer 1

No difference exists, whether those to be eaten are eaten  immediately after being selected individually, or all are selected randomly in succession and are set aside to be eaten later--what matters only is that each one is unavailable to be selected, once it has been removed from the bag.

 

a)  P(3 strawberry, 2 lemon) = 6C3•6C2 / 20C5

 

b) P(no lemons in 5 picks) = 14C5 / 20C5.

 

You can do the Arithmetic!