a The odds of an event occurring can be expressed as a ratio of the number of favorable outcomes to the number of unfavorable outcomes.
B
b Compare the numbers of favorable and unfavorable outcomes from Part A.
A
a 3:7
B
b 7:3
Practice makes perfect
a The odds of an event occurring can be expressed as the following ratio.
Number of favorable outcomes/Number of unfavorable outcomes
In order to find the odds in favor of drawing a red marble, we need to identify the number of favorable and unfavorable outcomes.
Number of favorable outcomes — the number of red marbles in the bag
Number of unfavorable outcomes — the number of marbles in the bag that are not red
We are given the probability of drawing a red marble from a bag of marbles.
P = 3/10
This probability tells us that the total number of marbles in the bag is 10. Out of those, 3 marbles are red. This means that we already know the number of favorable outcomes is 3. The number of unfavorable outcomes can by found by subtracting the number of red marbles form the total number of marbles in the bag.
10 - 3 = 7
We are ready to obtain the odds in favor of drawing a red marble.
3 : 7
b This time, we want to find the odds against drawing a red marble. In other words, the favorable outcome is not drawing a red marble. We first need to state the number of favorable and unfavorable outcomes.
Number of favorable outcomes — the number of marbles in the bag that are not red
Number of unfavorable outcomes — the number of red marbles in the bag
We know from Part A that of the 10 marbles in the bag, 3 are red and 7 are not. We are able to write the odds against drawing a red marble.
7 : 3
