Question

There are 36 gold cards and 36 silver cards in a deck. The gold cards are numbered 1,3,5,... 71 and the silver cards are numbered 2.4.6,... 72. The cards are throughly shuffled and one card is randomly selected.

A. Find the probability of selecting a gold card or a card with a multiple of 12 on it. Show your work

B. Find the probability of selecting a silver card or a card with a multiple of 9 on it. Show your work.

Answer 1

Explanation:

A.

Because there is no overlap between good card and card with a multiple of 12,

P(gold card or a card with a multiple of 12)

= P(gold card) + P(a card with a multiple of 12)

P(gold card)

= no. of gold cards / total no. of cards

= 36 / (36 + 36)

= 36 / 72

= 1/2

P(a card with a multiple of 12)

= no. of cards with multiples of 12 / total no. of cards

= (12, 24, 36, 48, 60, 72) / 72

= 6/72

= 1/12

P(gold card or a card with a multiple of 12)

= 1/2 + 1/12

= 7/12

B. There ARE overlaps between a silver card and a card with a multiple of 9,

P(silver card or a card with a multiple of 9)

= P(silver card) + P(a card with a multiple of 9) - P(silver card AND a multiple of 9)

P(silver card)

= no. of silver cards / total no. of cards

= 36 / (36 + 36)

= 36 / 72

= 1/2

P(a card with a multiple of 9)

= no. of cards with multiples of 9 / total no. of cards

= (9, 18, 27, 36, 45, 54, 63, 72) / 72

= 8/72

= 1/9

P(silver card AND a multiple of 9)

= no. of silver cards AND a multiple of 9 / total no. of cards

= (18, 36, 54, 72) / 72

= 4/72

= 1/18

P(silver card or a card with a multiple of 9)

= 1/2 + 1/9 - 1/18

= 10/18

= 5/9

Answer 2

A) multiples of 12 up to 72 ( 72 total cards)

12, 24, 36, 48, 60, 72 = 6 cards.

36 are gold.

Total gold cards and multiple of 12 = 36 + 6 =42

Probability of getting one of them is 42/72, which reduces to 7/12

B) 36 silver cards

Multiples of 9: 9, 18, 27, 36, 45, 54,63 = 7 cards

Silver cards are even and there is 3 even cards that are also multiples of 9, so subtract 3 from 7 to get 4.

Total silver cards and multiples of 9 = 36 + 4 = 40

Probability = 40/72 which reduces to 5/9