Answer to Question #153012 in Statistics and Probability for matia

Question

Two cards are draw at random from a well shuffled pack of 52cards. Find the probability that:
• Both are the same color
• Both are the different color

Answer 1

The deck has cards of two colors: red and black. The probability to draw a black color is $\frac{26}{52}=0.5$ and the same is the probability to draw a red color. The probability that two cards have a red color is: $\frac{26}{52}\cdot\frac{25}{51}\approx0.2451$. The same is the probability that two cards have a black color. We used the multiplication rule (https://www.statisticshowto.com/multiplication-rule-probability/) The probability cards have the same color is: $0.2451\cdot2=0.4902$. The probability that both cards have the different color is: $1-0.4902=0.5098$

Answer: the probability that two cards have the same color is: 0.4902; the probability that both cards have the different color is: 0.5098.