From a pack of 52 cards, a blackjack, a red queen and two black kings fell down. A card was then drawn from the remaining pack at random. Find the probability that the card drawn is (i) a black card (ii) a king
(iii) a red queen.
Solution:
Total number of cards = 52-4 = 48 [∵4 cards fell down]
So number of possible outcomes = 48
(i) Let E be the event of getting black card.
There will be 23 black cards since a black jack and 2 black kings fell down.
Number of favourable outcomes = 23
P(E) = 23/48
Hence the probability of getting black card is 23/48.
(ii) Let E be the event of getting a king.
There will be 2 kings remaining since 2 kings fell down.
Number of favourable outcomes = 2
P(E) = 2/48 = 1/24
Hence the probability of getting a king is 1/24.
(iii) Let E be the event of getting red queen.
There will be 1 red queen.
Number of favourable outcomes = 1
P(E) = 1/48
Hence the probability of queen is 1/48.
4/13If A and B denote the events of drawing a king and a spade card, respectively, then event A consists of four sample points, whereas event B consists of 13 sample points.
Thus,
\[P\left( A \right) = \frac{4}{52}\] and \[P\left( B \right) = \frac{13}{52}\]
The compound event (A ∩ B) consists of only one sample point, king of spade.
So,
\[P\left( A \cap B \right) = \frac{1}{52}\]
By addition theorem , we have:
P (A ∪ B) = P(A) + P (B) − P (A ∩ B)
= \[\frac{4}{52} + \frac{13}{52} - \frac{1}{52} = \frac{16}{52} = \frac{4}{13}\]
Hence, the probability that the card drawn is either a king or a spade is given by \[\frac{4}{13}\] .
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