Mathematics Project on Probability
Experiments on Probability
Objective: – To appreciate that finding probability through experiment is different from finding probability by calculation. Students become sensitive towards the fact that if they increase the number of observations, probability found through experiment approaches the calculated probability.
Description : (i) The teacher asked us to either work individually or at most in groups.
(ii) I collected the following data by visiting say 10 classrooms in the school.
(iii) I obtained the fraction of number of children having their birthday in the month of January, February,…………………………. December from the data given in the table.
(iv) I made a piediagram from the recorded data.
(v) I investigated that fraction actually obtained in step 3 tallies with the calculated probability obtained for each month.
If total no. of children whose birthday falls in month of January is 38 and the total number of students is 500.
The actual fraction of children born in January = 38/500 Probability for a child to have birthday in January = 31/365
(vi) The students increased the sample size, i.e. increased the number of observations and studied if the actual fraction approaches the calculated probability. I used a random sample for this purpose.
Calculation of probability by using formula (theoretical values)
31
Probability for a child to have Birthday in January =– = 0.08
365
29
Probability for a child to have Birthday in February (leap year) =– = 0.079
365
31
Probability for a child to have Birthday in March =– = 0.08
365
30
Probability for a child to have Birthday in April =— = 0.082
365
31
Probability for a child to have Birthday in May =— = 0.084
365
30
Probability for a child to have Birthday in June =– = 0.082
365
31
Probability for a child to have Birthday in July =– = 0.084
365
31
Probability for a child to have Birthday in August =– = 0.084
365
30
Probability for a child to have Birthday in September =— = 0.082
365
31
Probability for a child to have Birthday in October =— = 0.084
365
30
Probability for a child to have Birthday in November =— = 0.082
365
31
Probability for a child to have Birthday in December =– = 0.084
365
Table 1
Number of students having Birthday in various months in 1 class

No. of Students
Calculation of probability based on these observations (only 1 class of 61 students)
These are actual experimental values
Probability in month of January
_ favourable outcomes total outcomes
favourable%outcomes total%outcomes favourable%outcomes total%outcomes favourable%outcomes total%outcomes favourable%outcomes total%outcomes favourable%outcomes total%outcomes favourable%outcomes total%outcomes favourable%outcomes total%outcomes favourable%outcomes total%outcomes favourable%outcomes total%outcomes favourable%outcomes total%outcomes favourable%outcomes total%outcomes 
= ^{12} = 0.19
61 
= 0.06 = 0.16 = 0.05 = 0.03 
61
1 61 _ 3 61 _ 2 61 
= – = 0.16
61 = – = 0.15 61 = – = 0.05 61 = – = 0.09 61 
= 0.15 = 0.09 = 0.08 
61
6 61 _ _5_ 61 
Probability in month of February Probability in month of March Probability in month of April Probability in month of May Probability in month of June Probability in month of July Probability in month of August Probability in month of September Probability in month of October Probability in month of November Probability in month of December
Number of students having Birthday in various months in 2 classes

No. of students
Calculation of probability based on these observations (only 2 classes122 students)
These are actual experimental values
favourable outcomes total outcomes
favourable outcomes total outcomes favourable outcomes total outcomes favourable outcomes total outcomes favourable outcomes total outcomes favourable outcomes total outcomes favourable outcomes total outcomes favourable outcomes total outcomes favourable outcomes total outcomes favourable outcomes total outcomes favourable outcomes total outcomes 
= — = 0.09
122 
Probability in month of January
= 0.03 = 0.01 = 0.02 
122
1 122 3 122 
= — = 0.02
122 = — = 0.01 122 = — = 0.07 122 = — = 0.02 122 
= 0.05 = 0.07 = 0.05 
122
9 122 6 122 
= — = 0.04
122 
Probability in month of February Probability in month of March Probability in month of April Probability in month of May Probability in month of June Probability in month of July Probability in month of August Probability in month of September Probability in month of October Probability in month of November Probability in month of December
favourable outcomes total outcomes
Number of students having Birthday in various months in 10 classes

. . …. . .. _{c} favourable outcomes 74 – ~
Probability in month of January = ————— = — = 0.12
total outcomes 580
favourable outcomes 39
Probability in month of February = ——————— = — = 0.06
total outcomes 580
Probability in month of March = ^{favourable outcomes} = *L = 0.0*
total outcomes 580
Probability in month of April = ^{favourable outcomes} = H. = 0.05
total outcomes 580
Probability in month of May = ^{favourable outcomes} = ^ = 0.06
f nf n ? 1 1vi /l n COO
total outcomes 580
. ….. • .. r i favourable outcomes 42 
Probability in month of June = ——————– = — = 0.07
total outcomes 580
Probability in month of July = ^{favourable outcomes} = i^{8} = 0.08
total outcomes 580
46
favourable outcomes
Probability in month of August = —————— =—– = 0.07
total outcomes _{580}
51
favourable outcomes
Probability in month of September = —————— =— = 0.08
total outcomes _{580}
Probability in month of October = ^{favourable o}^^{comes}= = 0.08
total outcomes _{580}
60
favourable outcomes
Probability in month of November = —————— =—— = 0.10
total outcomes _{580}
58
favourable outcomes
Probability in month of December = —————— =—– = 0.1
total outcomes _{580}
Month  No. of children  Angle 
January  74  46 
February  39  24.2 
March  48  29.8 
April  29  18 
May  35  21.7 
June  42  26.1 
July  48  29.8 
August  46  28.6 
September  51  31.7 
October  50  31 
November  60  37.2 
December  58  36 
Total  580  360 
Observation ! – I observed that as the no. of students increases the experimental probability and that calculated with formula become almost equal.