A box is filled with 6 yellow cards, 2 green cards, and 4 blue cards. A card is chosen at random from the box. What is the probability that it is a yellow or a blue card?Write your answer as a fraction in simplest form.
Question
A box is filled with 6 yellow cards, 2 green cards, and 4 blue cards. A card is chosen at random from the box. What is the probability that it is a yellow or a blue card?Write your answer as a fraction in simplest form.
Solution
To solve this problem, we first need to determine the total number of cards. We do this by adding up the number of each type of card:
6 yellow cards + 2 green cards + 4 blue cards = 12 cards in total.
Next, we need to determine the number of favorable outcomes. In this case, a favorable outcome is drawing a yellow or a blue card. We add the number of yellow cards to the number of blue cards to find this:
6 yellow cards + 4 blue cards = 10 favorable cards.
The probability of an event is given by the ratio of the number of favorable outcomes to the total number of outcomes. In this case, the probability P(Yellow or Blue) is:
P(Yellow or Blue) = Number of favorable outcomes / Total number of outcomes P(Yellow or Blue) = 10 / 12
This fraction can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 2:
P(Yellow or Blue) = 10/2 / 12/2 P(Yellow or Blue) = 5/6
So, the probability of drawing a yellow or a blue card is 5/6.
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