A card is drawn at random from a standard deck of 52 cards. Find the following c

Question

A card is drawn at random from a standard deck of 52 cards. Find the following conditional probabilities. A) the card is a diamond, given that it is red B) the card is red, given that it is a diamond C) the card is a seven, given that it is red D) the card is a jack, given that it is a face card (Simplify your answer) A card is drawn at random from a standard deck of 52 cards. Find the following conditional probabilities. A) the card is a diamond, given that it is red B) the card is red, given that it is a diamond C) the card is a seven, given that it is red D) the card is a jack, given that it is a face card (Simplify your answer) A) the card is a diamond, given that it is red B) the card is red, given that it is a diamond C) the card is a seven, given that it is red D) the card is a jack, given that it is a face card (Simplify your answer)

Explanation / Answer

Solution

Part (A)

There are 26 red cards – 13 of Diamonds and 13 of Hearts.

So, conditional probability.the card is a diamond, given that it is red = 13/26 = ½ ANSWER

Part (B)

Since all Diamonds cards are red, conditional probability the card is red, given that it is a diamond = 1 ANSWER

Part (C)

There are 26 red cards – 13 of Diamonds and 13 of Hearts, and of these 26, there are two 7’s, namely 7 of Diamonds and 7 of Hearts. So, conditional probability.the card is a seven given that it is red = 2/26 = 1/13 ANSWER

Part (D)

Jack, Queen, King and Ace are the face cards. Since each suit, Clubs, Spades, Diamonds and Hearts, has 4 face cards, there are 16 face cards. Of these 16 face cards, 4 are Jack. Hence, conditional probability the card is a jack, given that it is a face card = 4/16 = ¼ ANSWER

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