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: $\frac{25}{102}$B: $\frac{25}{51}$C: $\frac{1}{2}$D: $\frac{2}{52}$I need help with how to get the answer

Answer 1

Answer:

The probability of picking two red cards is;

$P=\frac{25}{102}$

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;

$P=P_1\times P_2$

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;

$\begin{gathered} P_1=\frac{\text{ number of red cards}}{\text{total number of cards}}=\frac{26}{52} \\ P_1=\frac{26}{52}=\frac{1}{2} \end{gathered}$

The probability of picking red the second time is;

$P_2=\frac{25}{51}$

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;

$\begin{gathered} P=P_1\times P_2 \\ P=\frac{1}{2}\times\frac{25}{51} \\ P=\frac{25}{102} \end{gathered}$

Therefore;

The probability of picking two red cards is;

$P=\frac{25}{102}$