Use a stimulation of 20 families to estimate the probability

Use a stimulation of 20 families to estimate the probability of having at least 3 girls in a family of 5 children

Solution

Step 1: Describing outcomes

EIther child will be a girl or a boy.

Step 2: Since probability that a children either boy or girl will be equal. So the probability that a child will be a girl is 0.5. So 50% outcomes should represent the girl. There are total 10 different digits. Let 0,2,4,6,8 represent the girl and 1,3,5, 7, 9 represent the boy.

Step3 : Following are the random numbers of 5 digits generated by the random number generator :

78344, 31604, 81825, 45062, 41450, 10090, 80267, 25836, 99129, 83151, 17184, 35085, 95284 , 94687, 72576, 72809, 29914, 44698, 66444, 25108

Step 4:

Out of these 20 outcomes following are the outcomes that have at least 3 girls (that is, have at least 3 digits out of 0, 2, 4, 6, 8):

78344, 31604, 81825, 45062, 41450, 10090, 80267, 25836, 95284 , 94687, 72809, 44698, 66444, 25108

Step 5:There are 14 outcomes out of 20 which have at least 3 girls. So estimated probability is 14/20 = 0.7.