2022-04-14
A standard deck of cards contains 52 cards. One card is selected from the deck. (a) Compute the probability of randomly selecting queen or nine . (b) Compute the probability of randomly selecting queen or nine or king. (c) Compute the probability of randomly selecting nine or diamond.
nick1337
Expert2022-08-03Added 777 answers
A standard deck of cards contains 52 cards, where
26 cards are red, 26 cards are black
13 cards of each suit: Hearts, clubs, diamonds and spades
4 cards of each number/ character: A,2,3,4,5,6,7,8,9,10,J,Q,K
In the question, it is given that one card is randomly selected from the deck of 52 cards.
a. Find the probability of randomly selecting a 2 or queen.
A two can be selected in 4 ways (2 hearts or 2 of clubs or 2 of diamonds or 2 of spades).
Similarly, a queen can be selected in 4 ways.
Thus the probability of selecting a 2 or a queen is or 0.154
b. Find the probability of randomly selecting a 2 or a queen or a jack
A two can be selected in 4 ways (2 hearts or 2 of clubs or 2 of diamonds or 2 of spades).
Similarly, a queen can be selected in 4 ways.
Similarly, a jack can be selected in 4 ways.
Thus the probability of selecting a 2 or a queen or a jack is or 0.231
c. Find the probability of randomly selecting a ten or a diamond
A two can be selected in 4 ways (10 hearts or 10 of clubs or 10 of diamonds or 10 of spades).
A diamond can be selected in 13 ways. But, one of this is already a 10 (added above). Thus we will have only 12 ways of selecting a diamond (other than a ten).
Thus, the probability of selecting a ten or a diamond is or 0.308
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