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1.  In a certain country, the probability that a baby that is born is a boy is 0.52 and the probably that a baby that is born is a girl is 0.48. A family has two children. If X is the number of girls born to a family, find the probability that the family has 0, 1, or 2 girls.

(a)  Draw a tree diagram showing the possibilities for each outcome.

(b)  Create the binomial distribution table for p(x) .

 Jan 8, 2019
 #1
avatar+700 
+2

B = boy, G = girl

 

a) 
Probability of 2B is (0.52)(0.52) = 0.2704.
Probability of BG is (0.52)(0.48) = 0.2496 
Probability of GB is the same as the probability of BG, so it is 0.2496.
Probability of 2G is (0.48)(0.48) = 0.2304.

b) 
Number of girls born: 


Table for p(x) 
For zero girls and 2 boys, it is 0.2704.
For 1 girl and 1 boy, it is 0.4992.
For 2 girls, it is 0.2304. 

 

- PM

 #2
avatar+700 
+2

Here is the tree for  part a).

 

0 child              1st child              2nd child

                                                     | -- Boy (27.04%)

                           _ Boy (52%) -------[

Start                   |                          | -- Girl (24.96%)

    X -------------------|                          

                          |                          | -- Boy (24.96%) 

                          |_ Girl (48%) --------[

                                                     |_ Girl (23.04%)

 

- PM

edited by PartialMathematician  Jan 8, 2019
edited by PartialMathematician  Jan 8, 2019
 #3
avatar+103138 
+1

Excellent, PM....!!!!

 

 

cool cool cool

 Jan 9, 2019

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