Question 4 A card is selected at random from an ordinary pack of 52. If A = the card is an ace B = the card is from a black suit C = the card is a club D = the card is a diamond P = the card is a picture (Jack, Queen or King) R = the card is from a red suit (i) What are the values of the following? (a) P(A) (b) P(D) (c) P(A|D) (d) P(D|A)
Answers
Answer:
There are 52 cards in total.
Hence, total Outcomes =52
(i) Probability of the card drawn is a card of spade or an Ace:
Total cards of Spade =13
Total Aces =4
Number of Aces of Spade =1
Therefore,
Probability of the card drawn is a card of spade or an Ace:
52
13
+
52
4
−
52
1
=
52
16
=
13
4
(ii) Probability of the card drawn is a black king:
Total black kings: 2
Probability of the card drawn is a black king:
52
2
=
26
1
(iii) Probability of the card drawn is neither a jack nor a king
Total jacks =4
Total Kings =4
Probability of the card drawn is neither a jack nor a king:
1−
52
4+4
=
13
11
(iv) Probability of the card drawn is either a king or a queen:
Total Queens =4
Total Kings =4
Probability of the card drawn is either a king or a queen:
52
4+4
=
13
2