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A card is selected from a pack of 52 cards.
(a) How many points are there in this sample space?
(b) Calculate the probability that card is an ace of spades.
(c) Calculate the probability that the card is (i) an ace (ii) black card.
(a) How many points are there in this sample space?
(b) Calculate the probability that card is an ace of spades.
(c) Calculate the probability that the card is (i) an ace (ii) black card.
Solution:
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Verified Answer
(a) There are 52 cards. Therefore there are 52 points in the sample space.
(b) There is 1 ace of spade.
$\therefore n(A)=1, n(S)=52$
Probability that the card drawn is
an ace of spade $=\frac{n(A)}{n(S)}=\frac{1}{52}$
(c) (i) There are 26 black cards
$\therefore n(A)=24, n(S)=52$
$\therefore$ Probability of getting an ace card $=\frac{4}{52}=\frac{1}{13}$
(ii) There are 26 black cards.
$n(A)=26, n(S)=52$
Probability of getting a blacks cards
$=\frac{26}{52}=\frac{1}{2}$
(b) There is 1 ace of spade.
$\therefore n(A)=1, n(S)=52$
Probability that the card drawn is
an ace of spade $=\frac{n(A)}{n(S)}=\frac{1}{52}$
(c) (i) There are 26 black cards
$\therefore n(A)=24, n(S)=52$
$\therefore$ Probability of getting an ace card $=\frac{4}{52}=\frac{1}{13}$
(ii) There are 26 black cards.
$n(A)=26, n(S)=52$
Probability of getting a blacks cards
$=\frac{26}{52}=\frac{1}{2}$
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