Topic: PROBABILITY

Experimental Probability

A farmer asks, ‘Will it rain this month?’. The answer to the farmer’s question depends on three things; the months, the place where the farmer is, and what has happened in the past

three months in that place. The table below gives some answers to the question for different places and months.

 Place Month Answer to question Sokoto February No Jos July Ye Ibadan January Maybe Port Harcourt June yes

Is it possible to give a more accurate answer to a farmer near Ibadan in January? The table below shows that on average, 10mm of rain falls in Ibadan in January. However, this is an average found by keeping records over twelve years. The actual rainfall for Ibadan in January over the 12 years was as follows.

 J F M A M J J A S O N D Sokoto 0 0 0 10 48 91 155 249 145 15 15 0 Jos 3 3 28 56 203 226 330 292 213 41 3 3 Ibadan 10 23 89 137 150 188 160 84 178 155 46 10 Port Harcourt 66 109 155 262 404 660 531 318 516 460 213 81
 18 mm 0 mm 17 mm 9 mm 11 mm 22 mm 14 mm 0 mm 16 mm 0 mm 7 mm 6 mm

From the above data, it can be seen that rain fell in nine of the twelve months on January. If future years follow the pattern of the past, it is likely that in Ibadan, rain will fall in nine out of the next 12 Januaries. We say that the probability of rain falling in Ibadan in January is 9/12 (or ¾ or 0.75 or 75%). This probability can never be exact.  However, it is the best measure that we can give from the data we have. The number 9/12 is based on the experimental records. We say that it is experimental probability.

Example 1

A girl writes down the number of male and female children of her mother and father. She also writes down the number of male and female children of the parents’ brothers and sisters. Her resuts are shown in table below.

 Number of male children Number of female children Mother and father 2 5 Mother’s brother 6 8 Mother’s sister 4 8 Father’s brother 5 8 Father’s sister 7 7 Total 24 36

a. Find the experimental probability that when the girl has children of her own, her first born will be a girl.

b. If the girl eventually has five children, how many are likely to be male?