A card is drawn at random from a pack of 52 cards. Find the probability that the card drawn is:
(i) a spade
(ii) a black card
(iii) the seven of clubs
(iv) jack
(v) the ace of spades
Total number of outcomes, n(S) = 52
(i) n(E) = 2
∴ P(E) = \(\frac{n(E)}{n(S)}\) = \(\frac{2}{52}\) = \(\frac{1}{26}\)
(ii) n(E) = 26 + 2 = 28
∴ P(E) = \(\frac{n(E)}{n(S)}\) = \(\frac{28}{52}\) = \(\frac{7}{13}\)
(iii) n(E) = 2
∴ P(E) = \(\frac{n(E)}{n(S)}\) = \(\frac{2}{52}\) = \(\frac{1}{26}\)
(iv) n(E) = 12
∴ P(E) = \(\frac{n(E)}{n(S)}\) = \(\frac{12}{52}\) = \(\frac{3}{13}\)
(v) n(E) = 36
∴ P(E) = \(\frac{n(E)}{n(S)}\) = \(\frac{36}{52}\) = \(\frac{9}{13}\)
(vi) n(E) = 16
∴ P(E) = \(\frac{n(E)}{n(S)}\) = \(\frac{16}{52}\) = \(\frac{4}{13}\)
(vii) n(E) = 44
∴ P(E) = \(\frac{n(E)}{n(S)}\) = \(\frac{44}{52}\)
(viii) n(E) = 24
∴ P(E) = \(\frac{n(E)}{n(S)}\) = \(\frac{24}{52}\) = \(\frac{6}{13}\)
(ix) n(E) = 48
∴ P(E) = \(\frac{n(E)}{n(S)}\) = \(\frac{48}{52}\) = \(\frac{12}{13}\)
(x) n(E) = 4
∴ P(E) = \(\frac{n(E)}{n(S)}\) = \(\frac{4}{52}\) = \(\frac{1}{13}\)
(xi) n(E) = 13
∴ P(E) = \(\frac{n(E)}{n(S)}\) = \(\frac{13}{52}\) = \(\frac{1}{4}\)
(xii) n(E) = 26
∴ P(E) = \(\frac{n(E)}{n(S)}\) = \(\frac{26}{52}\) = \(\frac{1}{2}\)
(xiii) n(E) = 1
∴ P(E) = \(\frac{n(E)}{n(S)}\) = \(\frac{1}{52}\)
(xiv) n(E) = 4
∴ P(E) = \(\frac{n(E)}{n(S)}\) = \(\frac{4}{52}\) = \(\frac{1}{13}\)
(xv) n(E) = 1
∴ P(E) = \(\frac{n(E)}{n(S)}\) = \(\frac{1}{52}\)
(xvi) n(E) = 4
∴ P(E) = \(\frac{n(E)}{n(S)}\) = \(\frac{4}{52}\) = \(\frac{1}{13}\)
(xvii) n(E) = 13
∴ P(E) = \(\frac{n(E)}{n(S)}\) = \(\frac{13}{52}\) = \(\frac{1}{4}\)
(xviii) n(E) = 26
∴ P(E) = \(\frac{n(E)}{n(S)}\) = \(\frac{26}{52}\) = \(\frac{1}{2}\)
(xix) n(E) = 44
∴ P(E) = \(\frac{n(E)}{n(S)}\) = \(\frac{44}{52}\) = \(\frac{11}{13}\)
(i) a spade
Total numbers of cards are 52
Total number of spade cards = 13
Probability of getting spade is = \(\frac{Total\,number\,of\,spade\,cards}{Total\,number\,of\,cards}\) = \(\frac{13}{52}\) = \(\frac{1}{4}\)
(ii) a black card
Total numbers of cards are 52
Cards of spades and clubs are black cards.
Number of spades = 13
Number of clubs = 13
Therefore, total number of black card out of 52 cards = 13 + 13 = 26
Probability of getting black cards is = \(\frac{Total\,number\,of\,black\,cards}{Total\,number\,of\,cards}\) = \(\frac{26}{52}=\frac{1}{2}\)
(iii) the seven of clubs
Total numbers of cards are 52
Number of the seven of clubs cards = 1
Probability of getting the seven of clubs cards is = \(\frac{Total\,number\,of\,the\,seven\,of\,clubs\,cards}{Total\,number\,of\,cards}\)
= \(\frac{1}{52}\)
(iv) jack
Total numbers of cards are 52
Number of jack cards = 4
Probability of getting jack cards is = \(\frac{Total\,number\,of\,jack\,cards}{Total\,number\,of\,cards}\) = \(\frac{4}{52}=\frac{1}{13}\)
(v) the ace of spades
Total numbers of cards are 52
Number of the ace of spades cards = 1
Probability of getting ace of spades cards is = \(\frac{Total\,number\,of\,ace\,of\,spade\,cards}{Total\,number\,of\,cards}\)
= \(\frac{1}{52}=\frac{1}{52}\)