Page 221 - Algebra 1

Example
3
Calculating the Probability of Dependent Events
Natalia has two squares and three circles in a bag.
a. Find the probability of drawing a circle, keeping it, and then drawing another circle without the use of a tree diagram.
SOLUTION
For the first draw, the bag has 5 shapes and 3 are circles.
P(1st circle) = _3 5
For the second draw, a circle has been removed. There is one less circle and one less shape.
P(2nd circle) = _2 4
To find the probability of these two events, multiply their probabilities.
P(1stcircle)·P(2ndcircle)=_3·_2=_6 =_3 5 4 20 10
b. Find the probability of drawing a square, keeping it, and then drawing a circle.
SOLUTION
For the first draw, the bag has 5 shapes and 2 are squares.
P(square) = _2 5
For the second draw, a square has been removed. There is one less shape, but the number of circles is the same.
P(circle) = _3 4
To find the probability of these two events, multiply their probabilities.
P(square)·P(circle)=_2·_3=_6 =_3 5 4 20 10
Odds are another way of describing the likelihood of an event. Odds are expressed as a ratio, usually written with a colon. Odds can be calculated for something or against something happening.
Math Reasoning
Justify Why do both
the numerator and the denominator change for the second event?
Definition of Odds
Odds of an event: A ratio expressing the likelihood of an event. Assume that all outcomes are equally likely, and that there are m favorable
and n unfavorable outcomes.
The odds for the event are m:n. The odds against the event are n:m.
206 Saxon Algebra 1