An urn contains 10 red balls, 6 green balls, 15 orange balls, and 14 blue balls.
If one ball is randomly drawn from the urn, what are the odds against the ball being green?
State your answer as a ratio using a colon to separate the two numbers.
Prob (green) = 6/45 = 2/15
prob(not green) = 13/15
odds against the ball being green
---> odd in favour of not being green
= 13/15 : 2/15
= 13 : 2
To find the odds against a green ball being drawn, we need to determine the number of outcomes that are not in favor of drawing a green ball compared to the number of outcomes that are in favor of drawing a green ball.
First, let's calculate the total number of balls in the urn: 10 (red balls) + 6 (green balls) + 15 (orange balls) + 14 (blue balls) = 45 balls.
The number of outcomes in favor of drawing a green ball is simply the number of green balls in the urn, which is 6.
The number of outcomes not in favor of drawing a green ball is the sum of the balls that are not green, which is 10 (red balls) + 15 (orange balls) + 14 (blue balls) = 39.
So, the ratio of the odds against drawing a green ball can be expressed as 39:6.