The probability of a particular event may be deter-mined by knowing something about howthe event occursor how oftenit occurs. We know, for example, that the prob-ability of rolling a six-sided die (one member of a pair ofdice) and getting a four is , because the die has six sidesand any one side is equally likely to end up on top. So,in this case, understanding the nature of the event—theshape of the thrown die—allows us to determine the prob-ability. In other cases, we determine the probability ofan event by making a large number of observations. Whena weather forecaster says that there is a 40% chance of rainon a particular day, this probability was obtained by observ-ing a large number of days with similar atmospheric condi-tions and finding that it rains on 40% of those days. In thiscase, the probability has been determined empirically (byobservation).The multiplication rule Two rules of probability are use-ful for predicting the ratios of offspring produced in geneticcrosses. The first is the multiplication rule,which statesthat the probability of two or more independent eventsoccurring together is calculated by multiplying their inde-pendent probabilities.To illustrate the use of the multiplication rule, let’sagain consider the roll of dice. The probability of rollingone die and obtaining a four is . To calculate the probabil-ity of rolling a die twice and obtaining 2 fours, we can applythe multiplication rule. The probability of obtaining a fouron the first roll is and the probability of obtaining afour on the second roll is ; so the probability of rolling afour on both is (FIGURE3.7a). The key indi-cator for applying the multiplication rule is the word and;◗13616161616161615245215254Chapter 3(a)(b)TallShortTtTtTtTtTtttTallShortTtttTallShortGametesP generationF1generationttTtttFertilizationtTTtttConclusion: Genotypic ratio 1Tt:1ttPhenotypic ratio 1Tall:1Short3.6The Punnett square can be used fordetermining the results of a genetic cross.◗ConceptsThe Punnett square is a short-hand method ofpredicting the genotypic and phenotypic ratios ofprogeny from a genetic cross.
in the example just considered, we wanted to know theprobability of obtaining a four on the first roll anda four onthe second roll.For the multiplication rule to be valid, the events whosejoint probability is being calculated must be independent—the outcome of one event must not influence the outcomeof the other. For example, the number that comes up onone roll of the die has no influence on the number thatBasic Principles of Heredity55Roll 1Roll 2(a)The multiplication rule(b)The addition rule1If you roll a die,…1If you roll a die,…2…in a large number of samplerolls, on average, one out of sixtimes you will obtain a four…2…on average, one out ofsix times you'll get a three…3…and one out of sixtimes you'll get a four.