A card is drawn at random from a well shuffled deck of playing cards. Find the probability that the card drawn is a) a card of spade or an ace b) a black king c) neither jack or a king d)either queen or red
Answers
A card is drawn at random from a well-shuffled deck of playing cards. Find the probability that the card drawn is
i. a card of spade or an ace.
ii. a black king.
iii. neither a jack nor a king
iv. either a king or a queen.
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
All jacks, queens, and kings are removed from a pack of 52 cards. The remaining cards are well-shuffled and then a card is randomly drawn from it. Find the probability that this cards is (i) a black face card (ii) a red card