NAME



NAME ____________________

SECTION _________________

PROBABILITY - IT'S ALL IN THE TOSS OF A COIN!

Purpose: You will flip coins to simulate the random mixing of genes when offspring are produced. You will also use experimental results to decide if sample size affects how close you come to expected results and calculate percent deviation (a comparison tool).

Introduction: Probability is the chance that something can happen. This is expressed as a ratio, fraction, or percent. Calculating probability can give us good ideas of how genetic crosses will turn out. Mendel was very familiar with the laws of probability and these helped him define his genetic laws.

Materials: 2 coins (should be the same kind), calculator

Procedure: (Work in groups of two)

PART A: PROBABILITY AND PERCENT DEVIATION WHILE FLIPPING A SINGLE COIN

1. Toss a single coin 10 times and record the number of heads and tails below.

Heads ______ Tails______

2. Toss the coin 50 times. Keep a tally, then record the results below and in your assigned group number’s row on Chart A.

Heads _____ Tails ______

3. Calculate the percent deviation for your group using the method outlined below. Do this for both your 10-coin toss and your 50-coin toss. Percent deviation is the difference between observed and expected results. If percent deviation is small, it is probably due to chance; if it's large some unknown factors could have affected your results.

Q1. What are the expected numbers of heads for 10 tosses? Tails?

% Deviation = sum of differences from expected x 100

total occurrences

For example, a coin is tossed 10 times producing 7 heads and 3 tails. Calculate the deviation as follows:

OBSERVED EXPECTED DIFFERENCE FROM EXPECTED

Heads 7 5 2

Tails 3 +5 + 2

Totals 10 4

% Deviation = 4 x 100 = .4 x 100 = 40%

10

Q2. What is the percent deviation for your 10-toss trial? Your 50-toss trial?

4. Record your group results on the chart in the front of the room. Complete Chart A with the results of all the groups. Calculate the class results.

Q3. How does increasing the sample size (the total number of flips) affect

how close your actual results are to the expected results?

Q4. If you had 5,000 flips should your results be even closer to the expected

or further away?

PART B: TOSSING 2 COINS SIMULTANEOUSLY

Will tossing 2 coins at the same time affect the 50/50 outcome of Part

A? Do the laws of probability operate the same way when 2 events occur

independently of each other? In the second part of the lab we will be

investigating these two questions.

1. Let's take a look at the fraction method to determine the expected

outcomes of flipping 2 coins 40 times. PRODUCT RULE OF PROBABILITY =

THE PROBABILITY OF 2 EVENTS OCCURING TOGETHER IS THE

PRODUCT (X) OF THE PROBABLITIES OF THE SEPARATE EVENTS.

Here's what this means:

The chance that you can get a head with one flip is 1/2.

The chance of getting a head with the second flip is the same - 1/2.

So….. The chance of getting 2 heads while flipping 2 coins

is 1/2 x 1/2 = 1/4. Got it??

Q5. What's the probability of getting 2 tails when you flip 2 coins at the

same time?

Calculating the chance of getting heads/tails is a bit tricky. Don't forget that

technically when you flip 2 coins and get a heads/tails that the heads could

be first or the tails could be first. You have to take this into consideration

when you find the probability of flipping heads/tails. Confusing? YOU BET!!

First coin:

Chance of heads = 1/2, chance of tails = 1/2

1/2 x 1/2 = 1/4

Second coin:

Same thing - heads =1/2, tails = 1/2

Again 1/2 x 1/2 = 1/4

The chance of flipping a heads/tails with 2 coins flipped at once now becomes

1/4 (1st coin) + 1/4 (2nd coin) = 2/4 = 1/2. AMAZING!!

2. You are going to flip 2 coins together 40 times. Tally the results by

making slash marks in the chart below. But, before you do that, calculate

your expected results for 40 flips.

Expected results for 40 flips:

H/H = 40 x 1/4 = ____

T/T = 40 x 1/4 = ____

H/T = 40 x 1/2 = ____

H/H H/T T/T

| | | |

3. When you're finished flipping, record your results for your group number

on your Chart B and on the one in the front of the room. Complete your own Chart B for all the groups and record the class results.

Q6. Which came closer to the expected - your group or the class results?

Q7. So, one more time - why are the H/T expected results two times the

other two?

4. Don't forget that we can also use Punnett squares to predict genetic

probability. Sometimes, this is a lot easier and more practical than using all those fractions. Complete the Punnett squares below. (In the second square, notice that we've changed the H/T to T/t just like Mendel's tall or short pea plants!)

COINS PEA PLANTS

H T T t

H T

T t

Q7. What fraction of offspring should receive the genes tt?

Q8. If there is only 1 offspring, what the chance it could receive

the genes Tt?

WRAP-UP QUESTIONS:

1. Do Punnett squares tell you what must happen or what might happen?

Explain.

2. Why were class data important in this experiment?

3. If you get a small % deviation in an experiment does that mean something

went wrong?

4. If you flip 3 coins at the same time what is the probability that all 3 would be heads?

5. A wife and husband have 5 kids, all girls. What's the chance that the next child would be a girl? A boy? Explain.

6. A penny tossed 120 times results in 62 heads and 58 tails. In the space below, calculate the expected number of heads and tails and determine the % deviation.

CHART A

HEADS TAILS % DEVIATION

| GROUP | EXP | OBS | DIFF | EXP | OBS | DIFF | |

|1 | | | | | | | |

|2 | | | | | | | |

|3 | | | | | | | |

|4 | | | | | | | |

|5 | | | | | | | |

|6 | | | | | | | |

|7 | | | | | | | |

|8 | | | | | | | |

|9 | | | | | | | |

|10 | | | | | | | |

|11 | | | | | | | |

|12 | | | | | | | |

|13 | | | | | | | |

|14 | | | | | | | |

|CLASS | | | | | | | |

CHART B

HEADS/HEADS HEADS/TAILS TAILS/TAILS TOTAL

| GROUP | OBS | EXP | OBS | EXP | OBS | EXP | |

|1 | | | | | | | |

|2 | | | | | | | |

|3 | | | | | | | |

|4 | | | | | | | |

|5 | | | | | | | |

|6 | | | | | | | |

|7 | | | | | | | |

|8 | | | | | | | |

|9 | | | | | | | |

|10 | | | | | | | |

|11 | | | | | | | |

|12 | | | | | | | |

|13 | | | | | | | |

|14 | | | | | | | |

|CLASS | | | | | | | |

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