Question

A box contains 7 red, 14 yellow, 21 green, 42 blue, and 84 purple marbles. A marble is drawn at random from the box. Find the odds against drawing a purple or yellow marble.

A. 5 to 7


B. 5 to 12


C. 2 to 7

Answer 1

B

Explanation:

Here, we are to find the odds against drawing a purple or yellow marble.

Mathematically, the odds against drawing a particular marble color = 1 - the probability of drawing that particular marble color

probability of drawing a purple colored marble = number of purple colored marbles/total number of marbles

= 84/(84 + 42 + 21 + 14 + 7) = 84/168 = 1/2

So the odds against drawing a purple colored marble = 1 - 1/2 = 1/2

The odds against drawing a yellow marble color = 1 - probability of drawing a yellow colored marble

Probability of drawing a yellow colored marble = number of yellow marbles/total number of marbles = 14/168 = 1/12

So the probability of drawing a yellow colored marble or purple colored marble = 1/12 + 1/2 = 7/12

Now, the odds against drawing either of the two = 1 - the probability of drawing either of the 2 = 1 -7/12 = 5/12

or simply put 5 to 12