Lab: Probability
PURPOSE
To understand the fundamentals of probability and learn how to use the product rule.
INTRODUCTION
Take a chance! If 200 chances to win a guitar
were sold and you bought 10, what would be the probability that you would
win? Probability is expressed as a ratio: the number of times something
occurs (10) over the total number of possible occurrences (200). So, you
can calculate the
probability of winning by dividing 10 by 200. In this case, the probability
(p) would be p = 1/20,
or .05, or 5 percent. Probability is a numerical expression of the likelihood
that an event will occur.
PROCEDURE
A. Sample Size
When you toss a coin, what is the probability
that it will land with the head side up? The answer is 1/2, or .5, or
50 percent. In 10 throws you would expect to get 5 heads and 5 tails.
When you actually throw the coin, you may
not get a 5-heads:5-tails ratio. The difference between what you expect
according to probability and what happens is called the deviation. For
example, if you get 6 heads and 4 tails your deviation is 2 (1 from the
expected 5 heads plus1 from the expected 5 tails).
Deviation is normally expressed as a percent.
The percent deviation is calculated as follows: percent
deviation = _______deviation_______
total
number of occurrences
=
2/10 = .2 = 20 percent
1. Calculate the percent deviation for 3 heads and 7 tails out of 10 throws.
2. Toss a coin 10
times and record the results on the chart. Repeat the process for 9 more
trials
(of 10 throws each), making 100 throws
in all. Total the number of heads and of tails, and
calculate the percent deviation for the
entire 100 throws.
 |
Totals
= __________ ______________
Percent
deviation for 100 throws = _____________________
3. Would you expect the deviation for a sample size of 10 throws (trials
1-10) to vary to a greater degree
or to a lesser degree than the deviation for a sample size of 100 throws
(1-10 totals)?
4. Does the answer
to question 3 suggest to you that a smaller sample size or a larger sample
size improves the accuracy of your probability?
 |
* I don't know about you, but I'd call that a deviation.
B. The Product
Rule
The
product rule states the probability that two independent events will occur
simultaneously. Independent events are events that do not influence one
another. For example, if you roll two
dice, the number that comes up on one does not influence the number on
the other.
In this section you will use coins to discover the product rule of probability.
5. Flip 2 coins 100
times. Tally the results on the chart.
 |
6. What is the nearest
whole-number ratio of the results (two heads : one head and one tail :
two tails)? 1:1:1; 2:1:1; 1:2:1; 1:1:2;
or some other?
The probability of getting heads on the
first coin is ½ , or .5; and the probability of getting heads
on the second coin also is ½ . You can determine the probability
that both coins will come up
heads by multiplying the individual probabilities.
½ x ½ = ¼ , or .25
7. What is the probability of getting two tails on two coins?
8. What is the probability of getting a head on the first coin and a tail
on the second coin?
9. What is the probability of getting a tail on the first coin and a head
on the second coin?
Note that there are two ways of getting
1 head and 1 tail-the head first or the tail first. You
can find the probability of getting 1 head and
1 tail by adding the two individual probabilities.
First
Coin Second Coin
head
tail
p
= ¼
tail
head
p
= ¼
¼
+ ¼ = ½ . Thus p = ½ or .5
To summarize, the probability of getting
the different combinations of the two coins is:
2
heads p
= ¼ , or .25
1
head, 1 tail p
= ½ , or .50
2
tails p
= ¼ , or .25
10. Refer to the data
for your 100 throws of the two coins and calculate the percent deviation
from
the expected probability. First calculate
the number of occurrences of each combination
expected in 100 throws. Then calculate
the deviation between your results and the number
of occurrences.
a) Expected occurrences for 2 heads - _____
Percent
deviation for 2 heads = ___________
b) Expected occurrences for 1 head, 1 tail
= _____
Percent
deviation for 1 head, 1 tail = ___________
c) Expected occurrences for 2 tails = _____
Percent
deviation for 2 tails = ___________
Percent deviation for 100 throws = ___________
11. Calculate the
probability of the following independent events occurring simultaneously.
SHOW MATH.
a) Flipping 5 coins and all land heads.
b) Throwing 4 dice and getting all sixes.
c) Pulling an ace of spades twice in a row
(from 2 full decks of cards).
12. Complete the following
statement:
The Product Rule of Probability: To calculate
the probability that two independent events
will occur simultaneously, you …………………….
Applying Product Rule to Genetics:
13. Two parent plants,
hybrid for flower color are crossed. (Assume: R = red & r = white)
(Express ALL answers as fractions)
a) What is
the probability of producing a red egg?
b) What is
the probability of producing a white sperm?
(SHOW MATH)
c) What is
the probability of producing a pure red flower?
d) What is
the probability of producing a hybrid red flower?
e) What is
the probability of producing a white flower?
14. a) What is the
probability of producing a "RT" egg from a female "RrTt"
parent?
b) What is the probability of producing
a "RT" sperm from a male "RrTt" parent?
c) What is the probability of producing
a "RRTT" child from a cross of two "RrTt" parents?