Probability of the Occurrence of a Single Event Solution

Probability of the Occurrence of a Single Event

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Probability of the Occurrence of a Single Event

The law of probability states that when a procedure can result in two equally likely outcomes, the probability of either outcome occurring is1/2 or 50%.According to the law of probability, when there are four equally likely outcomes from a procedure, the probability that one of the outcomes will occur is1/4 or 25%. You can see how this is calculated. For example,

you know that in tossing two nickels, the probability of heads occurring on one nickel is1/2. The possibility of heads occurring on the other nickel is also1/2. The probability of heads occurring on both nickels in one toss is1/2×1/2=1/4.

You can use the probability to predict the probability of given genetic traits appearing in the offspring of particular parents. Punnett squares can also be used to obtain these results. When gametes are formed, the pair of alleles that determine a particular trait separate and one allele goes to each gamete. When fertilization occurs, a male and female gamete fuse.

The resulting zygote, which develops into the new individual, now contains two alleles for the trait. Which two of the parents’ alleles appear in the zygote is a result of chance? In this assignment, you will:

Predict the probability of the occurrence of a single event.

Predict the probability of two independent events occurring at the same time.

Apply Mendel’s law to predict the occurrence of certain traits in the offspring of parents exhibiting particular traits.

Apply the meaning of the term Standard Deviation to sampling techniques.

Instructions Your task is to complete each of the three parts of the activity on probability. Once completed you will answer an analysis question that relates the events of the activity to the inheritance patterns observed in Mendelian genetics. Materials For this activity, you will need the following:

Two nickels

Masking tape:Probability of the Occurrence of a Single Event

Part 1Part I: Probability of the Occurrence of a Single Event
1.     Toss a nickel 20 times. Count how many times it lands heads up and how many times it lands tails up. Write the totals under the observed column for 20 tosses in Table 1 below.2.     Using the law of probability, decide how many times out of 20 tosses you would expect heads to appear and how many times you would expect tails to appear. Write your answer

in the expected column for 20 tosses in Table 1 below.3.     Calculate deviation by subtracting the expected number from the observed number. Record these in the deviation column for 20 tosses in Table 1 below. Make all numbers positive.4.     Repeat Step 1, but tossing the nickel 30 times. Count how many times heads and tails appear. Record the observed

numbers in the observed column for 30 tosses in Table 1. 5.     Calculate the expected number of heads and tails and record them in the proper column in Table 1. Then calculate the deviates, and enter these in the proper column.6.     Repeat Step 1, tossing the nickel 50 times. Keep track of the appearance of heads and tails. Record the observed numbers,

expected numbers and deviations in the columns for 50 tosses in Table 1.7.     Calculate the standard deviation for each of the four sections above; 20, 30, 50 and total tosses. To calculate the standard deviation, first, subtract the expected from the observed, as done in Table 1 and then square this value. Divide this value by the number of events. Take the square

root of this result. This is your standard deviation. Enter your results in Table 2.Table 1: Probability of the Occurrence of a Single Event:HEADSTAILS20 TossesObservedExpectedDeviation30 TossesObservedExpectedDeviation50 Tosses Observed Expected Deviation Table 2: Standard Deviation of the Occurrence of a Single Event: Deviation from Table 1 Squared

Deviation divided by Number of Events Square Root of Previous Column (Standard Deviation)20 Tosses30 Tosses50 Tosses Part 2 :Probability of the Occurrence of a Single Event

Probability of Independent Events Occurring Simultaneously
1.     Toss two nickels 40 times simultaneously. Keep track of how many times heads-heads, heads-tails, tails-heads, and tails-tails occur. Count tails-heads and heads-tails together. Record the numbers for each combination in the observed column in Table 3 below.  2.     Calculate the percent of the total that each combination (heads-heads, heads-tails/tails-

heads, or tails-tails) occurred and record it in the proper column. To find the percent, divide each observed number by 40 and multiply by 100.  3.     Using the law of probability, predict the expected outcomes of tossing two nickels. Record the expected numbers in the proper column in Table 3.         Table 3: Probability of the Occurrence of Two Events           COMBINATIONS         OBSERVED         EXPECTED           Heads-Heads           Heads-Tails   Tails-Heads           Tails-Tails         Total   40   40    Part 3 : probability and mendelian genetics

1.     Place a small piece of masking tape on each side of two nickels. On one nickel write Ron each side. On the other nickel write r on each side.
2.     Toss the nickels several times. What combination of alleles always appear? Would the offspring with these genes be round or wrinkled?
3.     Replace the old tape with new tape. On each nickel, write Ron one side and r on the other side.
4.     Toss the coins simultaneously until all possible combinations of alleles have appeared. What combinations of genes appear? For each of the combinations, would the offspring be round or wrinkled?

Important:Probability of the Occurrence of a Single Event

Standard deviation tells how tightly a set of values is clustered around the average or expected outcomes of those same values. It’s a measure of dispersal, or variation, in a group of numbers. If a set of numbers is close to the average of those values or what is expected, then we may expect to see a low standard deviation. In contrast, if the set of numbers is spread across a greater range, it may present a high standard deviation. Higher standard deviation is often interpreted as higher volatility. In comparison, lower standard deviation would likely be an indicator of stability.

Analysis Questions

What trend could be observed between the observed and the expected outcomes.

In Part I, how did the standard deviation change as you increased the number of times you tossed the coin? How might you explain this observation?

In Part III, what combinations of alleles have appeared? For each combination, would the offspring be round or wrinkled?

Use the results of this activity on the law of probability to explain the law of independent assortment.

Probability of the Occurrence of a Single Event

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