Question

Mason has some number cards that each have a whole number on them. If he chooses a card at random, the probability that the number on it is even is 2/9 Work out the ratio of even cards to odd cards that Mason has. Give your answer in its simplest form.

Answer 1

The probability of choosing an even card being 2/9 indicates that out of 9 cards, 2 are even and 7 are odd, resulting in a ratio of even to odd cards of 2:7.

Step-by-step explanation:

If Mason chooses a number card at random and the probability that the number on it is even is 2/9, we can determine the ratio of even cards to odd cards that he has. Since the probability represents the favorable outcomes (even cards) over the total number of outcomes (all cards), we can set up a ratio where the number of even cards is 2 parts and the number of odd cards will make up the remaining parts of the total. Let's denote the number of odd cards as 'o' and the number of even cards as 'e' (which we know is 2 parts).

Since the probability of selecting an even card is 2/9, we know that out of every 9 cards, 2 are even, which means there must be 9 - 2 = 7 odd cards. Hence, the ratio of even cards to odd cards is 2 to 7. In the simplest form, this ratio is 2:7.

To conclude, the question asked to work out the ratio of even to odd number cards, which can be found using the given probability and understanding that the sum of the parts for even and odd must equal the total number of outcomes reflected in the probability.