Question

Researchers sampled 176 young women who recently participated in a STEM program. Of the 176 STEM​ participants, 107 were in urban​ areas, 56 in suburban​ areas, and 13 in rural areas. If one of the participants is selected at​ random, what is the probability that she is from an urban​ area? Not a rural​ area?

Answer 1

0.608

0.926

Explanation:

Total number of outcomes = Total number of women in the STEM program = 176

Number of favorable outcomes = The number of STEM​ participants in urban areas = 107

`\text {P(Woman is from an urban area)}=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\\\Rightarrow \text {P(Woman is from an urban area)}=\frac{\text{The number of STEM participants in urban areas}}{\text{Total number of women in the STEM program}}\\\Rightarrow \text {P(Woman is from an urban area)}=(107)/(176)\\\Rightarrow \text {P(Woman is from an urban area)}=0.608`

∴ The probability that she is from an urban​ area is 0.608

`\text {P(Woman is not from rural area)}=1-\frac{\text{The number of STEM participants in rural areas}}{\text{Total number of women in the STEM program}}\\\Rightarrow \text {P(Woman is not from rural area)}=1-(13)/(176)\\\Rightarrow  \text {P(Woman is not from rural area)}=0.926`

∴ The probability that she is not from a rural area is 0.926