Question

What is the probability of drawing a diamond from a standard deck of cards on a second draw, given that a diamond was drawn on the first draw and not replaced?

Answer 1

There are 52 cards in a deck of cards there 13th of each kind

So it's 13/52. X 12/52

Answer 2

The probability is 0.058.

Explanation:

Given : A standard deck of cards and a diamond was drawn on the first draw and not replaced.

To find : The probability of drawing a diamond from a standard deck of cards on a second draw, given that a diamond was drawn on the first draw and not replaced?

Solution :

`\text{Probability}=\frac{\text{Favorable outcome}}{\text{Total number of outcome}}`

In a standard deck of 52 cards,

13 diamonds , 13 club , 13 hearts , 13 spade

On a first drawn,

Favorable outcome (diamond was drawn) = 13

Total number of outcome = 52

Probability of first drawn is

`\text{Probability}=(13)/(52)`

On a second drawn given that first drawn is not replaced,

Favorable outcome (diamond was drawn) = 12

Total number of outcome = 51

Probability of second drawn is

`\text{Probability}=(12)/(51)`

Now, The probability of drawing a cards with the given situation is

`\text{Probability}=(13)/(52)*(12)/(51)`

`\text{Probability}=(156)/(2652)`

`\text{Probability}=0.058`

Therefore, The probability is 0.058.