Given:
The objective is to find,
a) The probability of selecting a king or a queen.
b) The probability of selecting a face card or a 10.
Explanation:
The total number of cards in a deck is, N = 52 cards.
a)
Out of 52 cards, the number of king cards is,
[tex]n(k)=4[/tex]Similarly, out of 52 cards, the number of queen cards is,
[tex]n(q)=4[/tex]Then, the probability of drawing one out of 4 king cards or one out of 4 queen cards can be calculated as,
[tex]\begin{gathered} P(E)=P(k)+P(q) \\ =\frac{n(k)}{N}+\frac{n(q)}{N} \\ =\frac{4}{52}+\frac{4}{52} \\ =\frac{8}{52} \end{gathered}[/tex]Hence, the probsability of selecting a king or a queen is (8/52).
b)
Out of 52 cards, the number of face cards is 12.
[tex]n(f)=12[/tex]Similarly, out of 52 cards, the number of 10 is,
[tex]n(10)=4[/tex]Then, the probability of drawing one out of 12 face cards or one out of 4 ten cards can be calculated as,
[tex]\begin{gathered} P(E)=P(f)+P(10) \\ =\frac{12}{52}+\frac{4}{52} \\ =\frac{12+4}{52} \\ =\frac{16}{52} \end{gathered}[/tex]Hence, the probability of selecting a face card or a 10 is (16/52).
c)
Out of 52 cards, the number of spade cards is 13.
[tex]n(s)=13[/tex]Similarly, out of 52 cards, the number of heart cards is 13.
[tex]n(h)=13[/tex]Then, the probability of drawing one out of 13 spade cards or one out of 13 heart cards can be calculated as,
[tex]\begin{gathered} P(E)=P(s)+P(h) \\ =\frac{n(s)}{N}+\frac{n(h)}{N} \\ =\frac{13}{52}+\frac{13}{52} \\ =\frac{26}{52} \end{gathered}[/tex]Hence, the probability of selecting a spade or a heart is 26/52.
d)
Out of 52 cards, the number of red cards is,
[tex]n(r)=26[/tex]Out of 52 cards, the number of black cards is,
[tex]n(b)=26[/tex]Then, the probability of drawing one out of 26 red cards or one out of 26 black cards is,
[tex]\begin{gathered} P(E)=P(r)+P(b) \\ =\frac{n(r)}{N}+\frac{n(b)}{N} \\ =\frac{26}{52}+\frac{26}{52} \\ =\frac{52}{52} \\ =1 \end{gathered}[/tex]Hence, the probability of selecting a red card or a black card is 1.
