a acard ia drawn at random from a well shufffled pack of 52 playing cards. Find the probability that the card drawn is (a) a spade or an ace (b) neither king nor queen

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Solution

Dear Student,

$(i) T o t a l S p a d e c a r d s = 13 w h i c h c o n t a i n s 1 A c e o f s p a d e N u m b e r o f A c e s i n a d e c k o f c a r d = 4 S i n c e 1 A c e o f s p a d e i s l a r e a d y i n c l u d e d i n S p a d e c a r d s S a m p l e S p a c e = 13 + 3 = 16 T o t a l C a r d s = 52 P r o b a b i l i t y t h a t a c a r d d r a w n i s s p a d e o r a n A c e = \frac{16}{52} = \frac{4}{13} (i i) N u m b e r o f K i n g s i n a d e c k o f c a r d = 4 N u m b e r o f Q u e e n s i n a d e c k o f c a r d = 4 S o, S a m p l e S p a c e = 4 + 4 = 8 P r o b a b i l i t y t h a t a c a r d d r a w n i s K i n g o r Q u e e n = \frac{8}{52} = \frac{2}{13} P r o b a b i l i t y t h a t t h e c a r d d r a w n i s n e i t h e r a q u e e n n o r a K i n g = 1 - \frac{2}{13} = \frac{11}{13}$

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