Question

A deck of cards contains 10 black cards and 10 red cards. The first card drawn is not replaced before drawing the second card. What is the probability of selecting a red card followed by a red card? 9 38 5 19 1 4 10 19 ​

Answer 1

9/38

Explanation:

P (1st card red) :

• No. of red cards / Total deck of cards
• 10 / 10 + 10
• 10/20
• 1/2

P (2nd card red) :

• No. of red cards - 1 / Total deck of cards - 1
• 10 - 1 / 20 - 1
• 9/19

P (both) :

• P (1st card red) x P (2nd card red)
• 1/2 x 9/19
• 9/38

Answer 2

Answer: 9/38

Reason:

There are 10 red cards out of 10+10 = 20 total.

10/20 = 1/2 is the probability of selecting a red card.

If the red card is not put back (i.e. "no replacement"), then the chances of getting another red card is (10-1)/(20-1) = 9/19

Multiply the two fractions mentioned to get the final answer.

(1/2)*(9/19) = (1*9)/(2*19) = 9/38