Question

3. A guidance counselor at a middle school collected the following information regarding the employment status of married couples within his Number of Children under 18 Years Old Worked 0 1 2 or More Total Husband Only L 172 79 174 425 Wife Only 94 17 15 126 Both Spouses 522 257 370 1149 Total 788 353 559 1700 For a-h write the probability statement, fraction, round to the fourth decimal place and state your solution in a complete sentence. a. (8 points) What is the probability that, for a married couple selected at random, both spouses work? b. (8 points) What is the probability that, for a married couple selected at random, the couple has one child under the age of 18? c. (8 points) What is the probability that, for a married couple selected at random, the couple has two or more children under the age of 18 and both spouses work? d. (8 points) What is the probability that, for a married couple selected at random, the couple has no children or only the husband works?

Answer 1

	0 child	1 child	2 or more children	Total
Husband Only	172	79	174	425
Wife only	94	17	15	126
Both spouses	522	257	370	1149
Total	788	353	559	1700

a) P(Both spouses work) = 1149/1700 = 0.6759

b) P(1 child) = 353/1700 = 0.2076

c) P(Both spouses work and 2 or more children) = 370/1700 = 0.2176

d) P(Only Husband work or 0 child) = P(Only Husband work) + P(0 child) - P(Only Husband work and 0 child)

= 425/1700 + 788/1700 - 172/1700 = 0.6124

e) P(Only wife works) = 126/1700 = 0.0741

no it will not be unusual as it is greater than 0.05.

f) P(2 or more children | Only wife works) = P(2 or more children and Only wife works) / P(Only wife works)

= (15/1700) / (126/1700) = 0.119

g) P(Only Husband work | 0 child) = P(Only Husband work and 0 child) / P(0 child)

= (172/1700) / (788/1700) = 0.2183