Question
I need help with Table 3
Principles of Probability but one head and one tail can be obtained in another way: The first coin could be tails and the second heads. Therefore, the fotal probability of obtaining a head on one coin an the other isThe chance for both coins to fall tails up is the same as for both to be heads, that is, 9To summarize, two coins tossed together many times are of the time; heads, tails (and vice versa) about of the time. Stated as a ratio instead of expected to fall heads, heads about of the time; and tails, tails about as fractions, the expected result is 1:221 2. Note that this situation is similar to what one sees in a simple monohybrid cross. When Ada produces gametes, the probability is that 1/2 of the gametes will contain the A allele and 1/2 wil contain a. When an Aa female is crossed with an Aa male and progeny are produced, the proba- bility is 1/4 that an A egg and an 4 sperm will come together to produce an 4A offspring. S occur simultaneously. Thus, a basic probability principle underlies Mende's first law expected ratios when three, four, or more coins are tossed together imi- larly, the probability is 1/2 for Aa and 1/4 for aa progeny. In studying this monohybrid cross, you are considering a situation in which independent events (the union of different kinds of gametes) 3. The same law of probability applied to the experiment with two coins can be used to calculate the a. For example, calculate the expected results from tossing three coins together. Let H represent the individual coins that fall heads and let T indicate tails for the same coins. Complete Table 3 showing the various possible combinations and the chances of their occurring. The first combi- nation of three heads, which can occur only one way, that is, when all three coins show heads, ked out as an example. Finally, toss three coins 64 times and record the frequency of is wor occurrence of each of the classes. Calculate the expected numbers and deviations b. A parallel situation would be observed were you to study families consisting of three childrern. ny would the three children be expected to be all boys? Two boys and a gir? One boy and two were to select randomly 160 families each of which had three children, in how ma you girls? Three girls? Table 3. Expected Results from Tossing Three Coins Together Write in the letters (H and T) to represent the coins in the Comb ability for each class resulting when three coins are tossed. Toss served numbers. inations" column, and calculate the prob- three coins 64 times to obtain the ob- Observed Number (O) Probability of Each Expected Number (E) Deviation Classes Combinations Class OccurringN O -E) 1/2 × 1/2 × 1/2 3 heads 2 heads: HHT, HTH, 31 T TH 2 tails 3 tails Totals lo 3
Explanation / Answer
When 3 coins are tossed, there are a total of 8 possibilities: HHH, HHT, HTH, THH, TTH, THT, HTT and TTT and each one of them are equally likely to occur.
Now lets try to complete the table 3 in the above problem:
Note that the total of all the observed number and the total of the expected number has to be 64 and the total deviation is 0.
Classes Combinations Probability of each occuring Observed Number (O) Expected Number(E) Deviation (O-E) 3 heads HHH 1/8 9 64/8 = 8 1 2 heads , 1 tail HHT, HTH, THH 3/8 28 3*64/8 =24 4 1 head, 2 tails TTH, THT, HTT 3/8 18 3*64/8 =24 -6 3 tails TTT 1/8 9 64/8 = 8 1 Total 64 64 0
