Module 6 Lesson 5 - 3 (Lab)
Lesson 5 — Probability
Lab — Calculating Probability
What are the chances of a person winning the Lotto 649 lottery? One chance in ten million? What are the chances of a person being struck by lightning? One chance in two million? If you are more likely to be struck by lightning than winning the lottery, then which should you be more concerned about?
Probability can be defined as a study of the chance that certain events or phenomena will happen. In this lab, you will explore how probabilities with coin tosses can be either linked or not linked. Then, you will draw connections between the outcomes
of coin tosses and the outcomes of genetic crosses.
Problem
The objective of this investigation is to study the probability associated with tossing coins.
In this exercise, you want to toss three consecutive heads when tossing one coin, or, to speed up the process, you can toss three coins together and attempt to get heads on all three coins on the same toss. Before you start, predict what your
chances are of getting heads on all three coins.
Materials
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paper
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a small cup
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pencil
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three coins of the same denomination
Procedure
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Place one coin in the cup. Cover the cup opening with your hand and shake the cup. Then, toss the coin on the table. Repeat 10 times. Record the number of heads and the number of tails you tossed.
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Using the same procedure, toss one coin 50 times. Record the number of heads and tails.
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Toss two coins at the same time 48 times using the same procedure as before. For each group of 8 tosses, record the number of double heads, one head one tail, and double tails that you tossed.
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Keep count of the number of attempts made until you toss the first set of three heads. Record the number of tosses it took. Try again and record the number of tosses.
Analysis
- How many tosses did you have to throw before you had three heads on a coin toss?
- How does your experimental result compare to the theoretical value that you calculated before you began the lab?
Because the probability of tossing a head on a coin toss is «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»1«/mn»«mn»2«/mn»«/mfrac»«/math», the probability of throwing three consecutive heads can be calculated by multiplying three probabilities: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»1«/mn»«mn»2«/mn»«/mfrac»«mo»§#160;«/mo»«mo»§#215;«/mo»«mo»§#160;«/mo»«mfrac»«mn»1«/mn»«mn»2«/mn»«/mfrac»«mo»§#160;«/mo»«mo»§#215;«/mo»«mo»§#160;«/mo»«mfrac»«mn»1«/mn»«mn»2«/mn»«/mfrac»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mfrac»«mn»1«/mn»«mn»8«/mn»«/mfrac»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mn»0«/mn»«mo».«/mo»«mn»125«/mn»«/math».
You may have noticed that the probabilities of tossing three tails, two heads and 1 tail, 1 head and 2 tails, and alternating combination of heads and tail are all the same: 0.125.
Conclusion
If you have ever had to guess a coin toss, the experience probably has taught you to appreciate the randomness of chance. In general, the more often an event occurs, the closer the actual frequency comes to the predicted frequency. Perhaps, you thought you knew the probability of an event occurring, but to your dismay it did not happen that way! Later, you discovered that you were lacking some key information. Consider the case in the next lesson.