1) FAMILY A family has 4 children. Assume that when a child...

1) FAMILY A family has 4 children. Assume that when a child is born, there is a 50% chance that the child is female. a) Determine the probabilities associated with the number of daughters in the family by calculating the probability distribution. b) What is the probability that the family has at least 3 daughters?

Transcript

00:01 Hello everyone we are going to solve a question in this question we are given that a family has four children so from here n is equals to from four and there is 50 % chance that the child is female so from here we have p is 0 .5 these two informations are given to us and here we consider that x denotes number of dotos in the family number of dotos in family so from here we consider that x denotes number of dotos in family so from here we consider the a different value of x from 0 to 4 and we calculate the probabilities in a part so in a part if this is a binomial distribution so the probability of x equals to x is equals to nc x p raised to the power x and here we have 1 minus p raised to the power n minus x so firstly from here we consider x equals to 0 x is equal to 0 that means probability x is 0.

01:00 Is equals to 4c0 0 .5 raised to the power 0 and 1 minus 0 .5 is 0 .5 raised to the power 4.

01:09 And on solving this is equal to 1 multiplied with 1 multiplied with 0 .5 raised to the power 4 which is equals to 0 .0 6 to 5.

01:22 This is the answer for x equals to 0.

01:26 Now we consider x is equal to 1.

01:29 So when x is equal to 1 probability that x is 1 is 4 c1 0 .5 raised to the power 1 point 5 raised to the power 4 minus 1 that is 3 and on solving this we have this value is equal to 4 multiplied with 0 .5 raised to the power 4 which is equals to 0 .25 and this is the answer when x is equal to 1 now we consider x is equal to 2 when x is equal to 2 the probability that x is 2 is given as 4c2 0 .5 raised to the power 2 and 0 .5 raised to the power 2.

02:07 So on solving this we have this is equal to 6 multiplied with 0 .5 raised to the power 4 and this is equals to 0 .375.

02:16 This is the answer when x is equals to 2.

02:19 Now moving ahead we consider x is equals to 3...

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