Question

A standard deck has 52 cards, and contains 13 cards of each of the four suites: diamonds, spades, hearts, and clubs. What is the probability that you choose a diamond, given that you have already chosen a diamond and have not replaced it?

a) 1/4
b) 13/51
c) 3/13
d) 4/17​

Answer 1

Option d)
`P=(4)/(17)`

Explanation:

we know that

The probability of an event is the ratio of the size of the event space to the size of the sample space.

The size of the sample space is the total number of possible outcomes

The event space is the number of outcomes in the event you are interested in.

so

Let

x------> size of the event space

y-----> size of the sample space

so

`P=(x)/(y)`

In this problem we have

`x=13-1=12`

`y=52-1=51`

substitute

`P=(12)/(51)`

Simplify

`P=(4)/(17)`