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Question
A card is drawn at random from a well-shuffled pack of 52 cards. Find the probability of getting
(i) a red king.
(ii) a queen or a jack.
Solution
Total number of cards in a pack = 52
∴ Number of possible outcomes = 52
(i) There are 2 red kings in a pack of cards such as king of heart and king of diamond.
Number of favourable outcomes = 2
Let E be the event that the card is red king.
`therefore P(E)=\text{Number of favourable outcomes}/\text{Number of possible outcomes}=2/52=1/26`
Thus, the probability of getting a red king is `1/26`.
(ii) There is one queen and one jack for each of spade, heart, club and diamond. Thus, there are 4 queens and 4 jacks in a pack of cards.
Number of favourable outcomes = 8
Let F be the event that the card is a queen or a jack.
`therefore P(f)=\text{Number of favourable outcomes}/\text{Number of possible outcomes}=8/52=2/13`
Thus, the probability of getting a queen or a jack is`2/13`
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