# Experimental vs. Theoretical Probability ```MBF3C Probability
Day 4
Warm Up: Write the following probabilities as Fractions, decimals and percents.
Fraction Decimal
Percent
What the probability of drawing a diamond from a
deck of 52 playing cards?
Jermaine has won 4 out of 10 races. What is the
probability that he will his next race?
A bag of marbles has 32 blue and 18 red marbles in it.
What is the probability of drawing a red marble?
Example 1
Determine the expected value for each of the following situations. Remember to express
the probability as a decimal before completing the calculation.
To determine the expected value:
a) The probability of producing a faulty part is 0.001. If 100 000 parts are produced,
how many might be expected to be faulty?
b) The probability that medication will cure a certain disease is 92%. From 300 patients
with this disease, how many might we expect to cure?
Example 2
a) How many times would you expect the spinner
to land on the 3 in 200 spins?
8 6
11
3
7
8
10
5
4
b) Mori plays a game with this spinner. He wins a dollar if the spinner lands on a
prime number and he loses a dollar if the spinner lands on an even number. Is this
a fair game? Explain.
Example 3 Theoretical vs. Experimental Probability
In a bag, there are 15 blue marbles and 10 red marbles. A marble is removed, the colour
is recored and then it is put back into the bag.
a) Use the frequency table below to draw a frequency distribution graph.
Result
Frequency
Blue
12
Red
18
b) State the theoretical probability of drawing a blue marble.
c) Sate the experimental probability of drawing a blue marble.
d) If the experiment were repeated for another 100 trials, how would you expect the
experimental probability of drawing a blue marble to change?
Day 4 Practice
Page 82 #1-5, 6c
Page 89 #2,3,5,6
Page 94 #6,7,10
1. A survey was conducted of voting intentions in a local election. In the survey,
1000 people were asked which political party they intended to vote for. Their
responses are shown in the table.
Conservative
320
Liberal
420
NDP
180
Other
80
a. What is the probability that a voter in the riding will vote NDP?
b. If there are 75 000 ballots cast in the election, how many people would
likely vote for the NDP?
2. Slug Fest has a batting average of 0.250. If he bats 4 times in today’s game, about
how many hits would you expect him to get?
3. The faces on a number cube are numbered 1, 1, 2, 3, 4, 4.
Sandy played a game with this cube. She won a dollar if she rolled a 2 or 3, but
had to pay a dollar if she rolled a 1 or 4. Is this a fair game? Explain. Use some
calculations to back up your explanation.
4. A lottery advertises a 1 in 12 chance of winning a cash prize. If 25 000 tickets
were sold, how many cash prizes are given out?
5. A die is tossed 20 times and it comes up as a three six times.
a. What is the theoretical probability of tossing a three?
b. What is the experimental probability of tossing a three?
1. a. 9/50
b.13,500
2. 1
3. Not a fair game. She is twice as likely to have to pay a dollar than to gain a dollar.
4. 2083
5. A. 1/6
b. 3/10
1.
In rolling a die, the theoretical possibility of rolling an odd number
a) State the theoretical probability of rolling an odd number with a die.
b) Roll a die 50 times. Complete the frequency chart.
Result
Tally
Frequency
Even
Number
Odd
Number
c) Calculate the experimental probability of an odd number based on the
above results.
d) How does the experimental probability of your die rolling results
compare to the theoretical probability of rolling an odd number?
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