(i) spade or an ace
Total numbers of cards are 52
Number of spade cards = 13
Probability of getting spade cards is = \(\frac{Total\,number\,of\,spade\,cards}{Total\,number\,of\,cards}\) = \(\frac{13}{52}\)
Total numbers of cards are 52
Number of ace cards = 4
Probability of getting ace cards is = \(\frac{Total\,number\,of\,ace\,cards}{Total\,number\,of\,cards}\) = \(\frac{4}{52}\)
Probability of getting ace and spade cards is = \(\frac{Total\,number\,of\,ace\,and\,spade\,cards}{Total\,number\,of\,cards}\) = \(\frac{1}{52}\)
Probability of getting an ace or spade cards is
= \(\frac{13}{52}+\frac{4}{52}-\frac{1}{52}=\frac{13+4-1}{52}=\frac{16}{52} =\frac{4}{13}\)
Therefore Probability of getting an ace or spade cards is = \(\frac{4}{13}\)
(ii) neither an ace nor a king
Total numbers of cards are 52
Number of king cards = 4
Number of ace cards = 4
Total number of cards = 4 + 4 = 8
Total number of neither an ace nor a king are= 52 – 8 = 44
Probability of getting neither an ace nor a king is = \(\frac{Total\,number\,of\,\,cards}{Total\,number\,of\,cards}\) = \(\frac{44}{52}=\frac{11}{13}\)
Therefore Probability of getting neither an ace nor a king is = \(\frac{11}{13}\)
(iii) neither a red card nor a queen
Total numbers of cards are 52
Red cards include hearts and diamonds
Number of hearts in a deck 52 cards = 13
Number of diamonds in a deck 52 cards = 13
Number of queen in a deck 52 cards = 4
Total number of red card and queen = 13 + 13 + 2 = 28,
[since queen of heart and queen of diamond are removed]
Number of card which is neither a red card nor a queen = 52 - 28 = 24
Probability of getting neither a king nor a queen is = \(\frac{Total\,number\,of\,\,cards}{Total\,number\,of\,cards}\) = \(\frac{24}{52}\) = \(\frac{6}{13}\)
Therefore Probability of getting neither a king nor a queen is = \(\frac{6}{13}\)
(iv) other than an ace
Total numbers of cards are 52
Total number of ace cards = 4
Total number of non-ace cards = 52-4 = 48
Probability of getting non-ace is = \(\frac{Total\,number\,of\,non\,ace\,cards}{Total\,number\,of\,cards}\) = \(\frac{48}{52}\) = \(\frac{12}{13}\)
(v) a ten
Total numbers of cards are 52
Total number of ten cards = 4
Probability of getting non-ace is = \(\frac{Total\,number\,of\,ten\,\,cards}{Total\,number\,of\,cards}\) = \(\frac{4}{52}=\frac{1}{13}\)
