Question

You choose a card from a deck of 52 cards. Without replacing the card, you choose a second card. What is the probability of choosing two red cards?A:
`(25)/(102)`B:
`(25)/(51)`C:
`(1)/(2)`D:
`(2)/(52)`I need help with how to get the answer

Answer 1

The probability of picking two red cards is;

`P=(25)/(102)`

Step-by-step explanation:

Given that;

You choose a card from a deck of 52 cards.

There are 26 red cards in a deck of 52 cards.

The probability of picking two red cards is;

`P=P_1* P_2`

where;

P1 and P2 are probability of picking red card the first time and the second time respectively.

The probability of picking red the first time is;

`\begin{gathered} P_1=\frac{\text{ number of red cards}}{\text{total number of cards}}=(26)/(52) \\ P_1=(26)/(52)=(1)/(2) \end{gathered}`

The probability of picking red the second time is;

`P_2=(25)/(51)`

Note: since there is no replacement the number of red cards and the total number of cards will reduce by 1.

The overall probability will then be;

`\begin{gathered} P=P_1* P_2 \\ P=(1)/(2)*(25)/(51) \\ P=(25)/(102) \end{gathered}`

Therefore;

The probability of picking two red cards is;

`P=(25)/(102)`