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Making Predictions
10-5
Vocabulary
Prediction- something you can
reasonably expect to happen in
the future.
A prediction is something you can
reasonably expect to happen in the future.
Weather forecasters use several different
methods of forecasting to make predictions
about the weather.
One way to make a prediction is to use
probability.
Additional Example 1: Using Experimental
Probability to Make Predictions
Lawrence finds the experimental probability of
his reaching first base is 40%. Out of 350 atbats, how many times can he expect to reach
first base?
Method 1: Set up an equation.
4
· 350 = x
10
140 = x
Multiply the probability by the number
of at bats.
Additional Example 1 Continued
Method 2: Set up a proportion.
x
4
=
350
10
4 · 350 = 10 · x
1400 = 10x
10
10
140 = x
Think: 4 out of 10 is how many out
of 350.
The cross products are equal.
Multiply.
Divide each side by 10 to isolate the
variable.
Lawrence can predict that he will reach first base about
140 of 350 times.
Check It Out: Example 1
Malia finds the experimental probability of her
scoring a goal is 20%. Out of 225 attempts,
how many times can she expect to score a
goal?
Additional Example 2: Using Theoretical Probability
to Make Predictions
A spinner has eight sections of equal size.
Three sections are labeled 1, two are labeled 2,
and the others are labeled 3, 4, and 5. In 50
spins, how often can you expect to spin a 1?
P(spinning a 1) = 3
8
Think: 3 out of 8 is how many
3
x
=
out of 50.
8
50
3 · 50 = 8 · x
The cross products are equal.
150 = 8x
8
8
Multiply
Divide each side by 8 to isolate
the variable.
You can expect to spin a 1
about 19 times.
18.75 = x
Helpful Hint
Round to a whole number if it makes
sense in the given situation.
Check It Out: Example 2
A spinner has eight sections of equal size.
Three sections are labeled 1, two are labeled 2,
and the others are labeled 3, 4, and 5. In 50
spins, how often can you expect to spin a 2?
Additional Example 3: Problem Solving Application
The Singh family is planning a 7-day
tropical vacation during July or August. The
island destination they have chosen
averages 21 rainy days during this 62-day
period. If the Singhs would like to avoid
rain on at least 5 days of their vacation,
should they go to this spot or choose
another?
Additional Example 3 Continued
1
Understand the Problem
The answer will be whether the Singh family
should go to the island.
List the important information:
The island destination averages 21
rainy days out of 62 days.
•
The Singhs want to avoid rain on at least 5
days of their vacation.
•
Additional Example 3 Continued
2
Make a Plan
On average 21 out of the 62 days it is rainy. After
finding out the number of rainy days there should
be forecast, subtract to find the number of not
rainy days.
Additional Example 3 Continued
3
Solve
x
21
=
7
62
Think: 21 out of 62 is how many out of 7.
21 · 7 = 62 · x The cross products are equal.
147 = 62x
62
62
2.37 ≈ x
7–2=5
Multiply.
Divide each side by 62 to isolate the
variable.
There will be more than 2 rainy days
in 7 days.
Subtract the predicted number of rainy
days from the total vacation days.
Additional Example 3 Continued
4
Look Back
They should choose a different location. It is
likely to rain more than 2 days (about 2.4 days)
during a 7-day period, which will not give the
Singhs at least 5 sunny days.
21 rainy days ≈ 20 or 33%
62 total days
60
2.4 rainy days ≈ 2 or 30%
7 total days
7
Since both ratios are about 30%, the answer is
reasonable.
Check It Out: Example 3
The Reid family is planning a 9-day winter
vacation during December or January. The
destination they have chosen averages 35
snow days during this 60-day period. If the
Reids would like to avoid snow on at least
4 days of their vacation, should they go to
this spot or choose another?