A hint to get started
Condition the multi-pack card sample on its suit counts
A set of 40 cards is assembled from several ordinary packs, with counts:
| Rank | Spades | Hearts | Diamonds | Clubs |
|---|---|---|---|---|
| King | 3 | 2 | 6 | 4 |
| Queen | 4 | 5 | 4 | 1 |
| Jack | 1 | 3 | 2 | 5 |
For example, there are 4 Kings of Clubs and 3 Jacks of Hearts. Three cards are drawn at random without replacement.
(i) Find the probability they are three Kings, three Queens or three Jacks. marks
(ii) Given two Spades and one Diamond are drawn, find the probability they are three Kings, three Queens or three Jacks. For example, two Kings of Spades and one King of Diamonds qualify. marks
[2014/TPJC/II/8]
CJC · Review problems · Question 16
In(ii), use a denominator counting exactly two Spades and one Diamond.