A standard deck of cards contains 52 cards.

Answered question

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.

Answer & Explanation

nick1337

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 4+452= 852= 213= 0.1538462 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 4+4+452= 1252= 313= 0.2307692 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 4+1252= 1652= 413= 0.3076923 or 0.308

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