A box is filled with 3 red cards, 2 green cards, and 9 yellow cards. A card is chosen at random from the box. What is the probability that it is a red or a yellow card.

Answer 1

P(red) = (number of red cards) / (total number of cards) = 3 / (3+2+9) = 3/14

P(yellow) = (number of yellow cards) / (total number of cards) = 9/14

P(red or yellow) = P(red) + P(yellow) (since the selection of red or yellow cards are independent, we can just add them straight away):

P(red or yellow) = 3/14 + 9/14 = 12/14 (reduces to 6/7)

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Another way to go with this is to look at the complementary situation: if the card is red or yellow then it is NOT green.

We first need to find the probability of selecting green, then use the fact that we must select green or NOT green with probability equal to 1 (i.e. it is 100% certain we choose green or not green). To find the probability of the card being green, we take the number of green cards (2) and divide by the total number of cards (14):

P(green chosen) = 2/14

Now, the card chosen is either green or it is NOT green (in this case "not green" is the same as "yellow or red selected"), and these must sum to 1.

P(not green) + P(green) = 1

Plug in calculated value:

P(not green) + 2/14 = 1

Subtract 2/14 from each side (subtracting 2/14 from both sides preserves the equality of both sides):

P(not green) = 1 - 2/14

P(not green) = 12/14 = 6/7 (same answer as before, as expected)

Answer 2

Finding the probability that the card is red or yellow means we are looking for the non-green card.

Non-green cards = 3+9 = 12

Total # of cards = 3+2+9 = 14

Probability = (3+9)/ 14 = 12/14 = 6/7