Answer to Question #186841 in Algebra for Daniela(me)

Question

Pew Research Center reported that among mothers, family size is shrinking. Suppose we are to randomly select one mother (age 40 to 44) and record the number of children she has. Here is a probability model.

 

Number of Children

1

2

3

4+

Probability

0.22

0.41

0.24

0.13

 

(a) Explain why this is a valid probability model.

 

(b) Explain why events “have 1 child” and “have 2 children” are mutually exclusive

 

 

 

For each of the following write the event using proper notation and find the probability:

(c) Find the probability that a randomly selected mother has less than 2 children.

 

 

(d) Find the probability that a randomly selected mother has 1 or 2 children. 

 

 

(e) Find the probability that a randomly selected mother does not have 4 or more children.

 

Answer 1

A) This is a valid probability model because is a mathematical representation of a Chance occurrence

B) Event "have 1child"and "have 2 children" are mutually exclusive if they can not occur at the same time

C) the probability of selected mother has less than 2 children= total number of children is 10, (2/10×1/10) = 1/50ans

D) The probability of randomly selected mother has 1or 2 children= (1/10+2/10) = 3/10ans

E) probability that a randomly selected mother does not have 4 or more children= (1/10×0.22)×(2/10×0.41)×(3/10×0.24)×(4/10×0.13)= (0.022)×(0.082)×(0.072)×(0.052) = 6.754×10^-6 ans