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PolarNik [594]
3 years ago
8

A card is drawn at random from a standard deck of 52 cards. Find the following conditional probabilities. ​a) The card is a diam

ond​, given that it is red. ​b) The card is red​, given that it is a diamond. ​c) The card is a nine​, given that it is red. ​d) The card is a king​, given that it is a face card.
Mathematics
1 answer:
Inga [223]3 years ago
7 0

Answer:

a.\frac{1}{13}\\b.\frac{1}{2}\\c.\frac{1}{13}\\d.\frac{1}{13}

Step-by-step explanation:

P(A|B) = P(A and B) / P(B)

Total number of cards = 52

a)

Let A denotes the event that the card is a diamond​ and B denotes the card is red.

P\left ( A|B \right )=\frac{P\left ( A\cap B \right )}{P(B)}\\=\frac{\frac{2}{52}}{\frac{26}{52}}\\=\frac{1}{13}

b)

Let A denotes the event that the card is red​ and B denotes the card is diamond.

P\left ( A|B \right )=\frac{P\left ( A\cap B \right )}{P(B)}=\frac{\frac{2}{52}}{\frac{4}{52}}\\=\frac{1}{2}

c)

Let A denotes the event that the card is nine and B denotes the card is red.

P\left ( A|B \right )=\frac{P\left ( A\cap B \right )}{P(B)}=\frac{\frac{2}{52}}{\frac{26}{52}}\\=\frac{1}{13}

d)

Let A denotes the event that the card is a king and B denotes the card is a face card.

P\left ( A|B \right )=\frac{P\left ( A\cap B \right )}{P(B)}=\frac{\frac{4}{52}}{\frac{12}{52}}\\=\frac{1}{13}

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