Question

The red face cards and the black cards numbered 4-9 are put into a bag. Three cards are drawn at random without replacement. Find the following probability:

At least 1 of the cards is red.

Answer 1

Number of red face cards = 3 + 3 = 6 (king, queen and jack)

Number of black cards numbered 4-9 = 6 + 6 = 12

Total number of cards that are put into a bag = 6 + 12 = 18

The probability that at least 1 of the cards is red

= 1 - P( no card is red)

= 1 - P( all three cards are black)

$= 1 - \frac{12*11*9}{18*17*16}$