PROBABILITYPROBABILITY(Theoretical)(Theoretical)

Predicting Outcomes

What is probability?

Probability refers to the chance that an event will happen.

Probability is presented as the ratio of the number of ways an event can occur relative to (over) the number of possible outcomes.

Probability of Event =Number of ways an event can occur

Number of possible outcomes

Example 1If you roll a die, what’s the probability of rolling a

four?

Probability of Event = Number of ways an event can occur

Number of possible outcomes

P(4)= There is only 1 four on a die =

6 possible outcomes (one, two, three, four, five, and six)

P(4) = 1 6

Example 2If you roll a die, what’s the probability of rolling a

number less than 4?Probability of Event = Number of ways an event can occur Number of possible outcomes

P(less than 4)=There are 3 ways the event can occur: {1,2,or 3}=

Number of possible outcomes: {1,2,3,4,5,or 6}

P(Less than 4)= 3 = 1 6 2

Example 3If you pick from a bag that contains 5 blue marbles, 2 green

marbles, and 3 red marbles, what’s the probability of picking a red marble?

Probability of Event =Number of ways an event can occur

Number of possible outcomes

P(red marble)= There are 3 red marbles in the bag There are 10 possible outcomes (5 blue + 2 green + 3

red)P(red marble)= 3 10

Your Turn1) You roll a number cube numbered from

1 to 6. P(an even number) = 2) A jar contains 17 navy and 20 green

marbles. A marble is drawn at random.P(not navy) =

3) A number from 20 to 29 is drawn at random.P(a composite number) =

4) A number from 23 to 33 is drawn at random.P(a number divisible by 3) =

Complementary events

• Complementary events are two events in which either one or the other must happen, but both cannot happen at the same time.

• The sum of the probabilities of complementary events is 1.

There is a 25% chance that Sam will win a prize. What is the probability

that Sam will not win a prize?• The sum of the probabilities of

complementary events is 1. • P(win) + P(not

win) = 1

• Replace P(win) with 0.25.• 0.25 + P(not win) = 1

• Subtract 0.25 from each side.

• 0.25 + P(not win) = 1

• -0.25 -0.25

• P(not win) = 0.75

• So, the probability that Sam won’t win a prize is 0.75, 75%, or ¾ .