A card is drawn from a well-shuffled pack of 52 cards. Find the probability of getting:
(xi) neither a spade nor a jack
(xii) neither a heart nor a red king
(xi) Let E be the event of getting a neither a spade nor a jack.
There are 13 spades and 3 other jacks. So remaining cards = 52-13-3 = 36
There will be 36 cards which are neither a spade nor a jack.
Number of favourable outcomes = 36
P(E) = 36/52 = 9/13
Hence the probability of getting a neither a spade nor a jack is 9/13.
(xii) Let E be the event of getting a neither a heart nor a red king.
There are 13 heart cards and 1other red king. So remaining cards = 52-13-1 = 38
There will be 38 cards which are neither a heart nor a red king.
Number of favourable outcomes = 38
P(E) = 38/52 =19/26
Hence the probability of getting a neither a heart nor a red king is 19/26.
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