Question

A standard​ 52-card deck has four​ 13-card suits:​ diamonds, hearts,​ clubs, and spades. The diamonds and hearts are​ red, and the clubs and spades are black. Each​ 13-card suit contains cards numbered from 2 to​ 10, a​ jack, a​ queen, a​ king, and an ace. An experiment consists of drawing 1 card from the standard deck. Find the probability of drawing a black five of diamonds.

Answer 1

The probability of drawing a black five of diamonds from a standard deck is 0.0002.

Step-by-step explanation:

Identify relevant sets:

Total cards in the deck: 52

Black cards: 26 (clubs and spades)

Five cards: 4 (one in each suit)

Black five of diamonds: 1

Calculate the probability:

Probability of drawing a black card: 26 black cards / 52 total cards = 13/26

Probability of drawing a five: 4 five cards / 52 total cards = 1/13

Combine probabilities (independent events):

Since drawing the card color and the card number are independent events, we multiply their probabilities:

Probability of drawing a black five of diamonds = (13/26) * (1/13) = 1/52 = 0.0192

Adjust for specific card:

There is only one black five of diamonds, so the final probability is the probability of drawing any black five multiplied by the number of black fives:

Probability of drawing a black five of diamonds = 0.0192 * 1 = 0.0002

Therefore, the probability of drawing a black five of diamonds from a standard deck is 0.0002.

Answer 2

Probability of drawing a black five of diamonds= 0

Step-by-step explanation:

Given,

Total number of cards, n(B) = 52

Number of diamonds cards = 13

Number of hearts cards = 13

Number of clubs cards = 13

Number of spades cards = 13

Since,the diamonds and hearts are​ red, and the clubs and spades are black.

So, the number of card which is black diamond = 0

So,the number of black five of diamonds, n(A) = 0

So, the probability of drawing a black five of diamonds is,

`P(A)\ =\ (n(A))/(n(B))`

`=\ (0)/(52)`

= 0

So, the probability of drawing a black five of diamonds is zero.