Two cards are drawn together at random from a well-shuffled pack of 52 playing cards. What is the probability that both cards are red?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(\frac{25}{102}\)
A pack has 26 red cards (hearts and diamonds). Drawing two cards is a selection, so P(both red) \(=\) ways to choose 2 red ÷ ways to choose any 2.
Ways to choose 2 red \(\displaystyle ={}^{26}C_2=\frac{26\times25}{2}=325\)
Ways to choose any 2 \(\displaystyle ={}^{52}C_2=\frac{52\times51}{2}=1326\)
Probability \(\displaystyle =\frac{325}{1326}=\frac{25}{102}\)