what is the probability of drawing a 9 or diamond from a standard deck of cards?

In a standard deck of cards, there are 52 cards. They are broken down into suits (4 of them: Spades, Hearts, Diamonds, Clubs) of 13 cards each. Each suit has 13 ordinal cards (A, 2 through 10, Jack, Queen, King).

Here we're asked to draw a card at random and find the probability of drawing either a diamond or a 9.

With probability, we look at the fraction of ways we can achieve some condition (the numerator) over the number of ways we can do something (the denominator).

Our denominator here is 52 - the number of cards from which we can pull 1.

Our numerator is both all the diamonds, 13 cards, and all the nines, 4 cards, but we need to subtract 1 to account for the double counting of the 9 of diamonds.

In all we get:

13+4 - 1/52 =

≈ 16/52

=4/13

Answer: 0.3077

MrRoyal MrRoyal · Answer 2 · 2021-09-02T13:43:10+02:00

Probabilities are used to determine how likely an event is, to happen. The probability of drawing a 9 or diamond is: 4/13

In a standard deck of cards, we have:

[tex]n = 52[/tex] --- There are 52 cards in total

[tex]n(9) = 4[/tex] ---- Cards with number 9 are 4

[tex]n(Diamond) =13[/tex] ---- there are 13 diamonds

[tex]n(9\ n\ Diamond) = 1[/tex] ---- Diamond cards with number 9

The probability of drawing a 9 or diamond is:

[tex]P(9\ or\ Diamond) = P(9) + P(Diamond) - P(9\ n\ Diamond)[/tex]

So, we have:

[tex]P(9\ or\ Diamond) = \frac{n(9)}{n} + \frac{P(Diamond)}{n} - \frac{n(9\ n\ Diamond)}{n}[/tex]

This gives:

[tex]P(9\ or\ Diamond) = \frac{4}{52} + \frac{13}{52} - \frac{1}{52}[/tex]

Take LCM

[tex]P(9\ or\ Diamond) = \frac{4+13-1}{52}[/tex]

[tex]P(9\ or\ Diamond) = \frac{16}{52}[/tex]

Simplify

[tex]P(9\ or\ Diamond) = \frac{4}{13}[/tex]

Hence, the probability of drawing a 9 or diamond is: 4/13