Re: If two cards are picked out of a standard 52-card deck of cards, witho
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Updated on: 16 Aug 2022, 10:33
If two cards are picked out of a standard 52-card deck of cards, without replacement, what is the probability that the cards picked are of two different suits ? (A standard 52-card deck of cards has four suites: hearts, clubs, spades, diamonds (13 cards in each suit).)
A. 15/17
B. 13/17
C. 11/17
D. 4/17
E. 13/102
There are 4 cases possible
ie, First pick can be either a Heart / Club / Spade / Diamond (all equally probable)
(say) Probabilty (pick a Heart) = 13/52 = 1/4
Without replacement,
Probability (pick a Card, which is NOT a Heart) = 39/51 = 13/17
(39 cards ie, 13*3 belong to Club / Spade / Diamond; while Total cards remaining =51)
Hence, Total probability (when Heart is chosen as the first pick) = (1/4) * (13/17)
Similarly,
Total probability (when Spade is chosen as the first pick) = (1/4) * (13/17)
Total probability (when Club is chosen as the first pick) = (1/4) * (13/17)
Total probability (when Diamond is chosen as the first pick) = (1/4) * (13/17)
Since all the aforementioned events are mutually exclusive, Overall probability = 4 * (1/4) * (13/17)
= 13/17
Correct option is (B)
Originally posted by
pintukr on 29 Jul 2022, 06:38.
Last edited by
pintukr on 16 Aug 2022, 10:33, edited 1 time in total.