According to the 2000 U.S. Census Bureau, 49.65% of Texas residents were male. If one Texan was selected at random in 2000, what is the probability she was female?
a. 0.4965
b. 0.5
c. 0.5035
d. 49
Answer (1)
The probability of selecting a male Texan is given as P ( M ) = 0.4965 .
The probability of selecting a female Texan is P ( F ) = 1 − P ( M ) .
Calculate P ( F ) = 1 − 0.4965 = 0.5035 .
The probability that a randomly selected Texan in 2000 was female is 0.5035 .
Explanation
Understand the problem We are given that in 2000, 49.65% of Texas residents were male. We want to find the probability that a randomly selected Texan in 2000 was female.
Define events and probabilities Let M be the event that the selected Texan is male, and F be the event that the selected Texan is female. We are given that the probability of selecting a male, P(M), is 0.4965.
Use the fact that probabilities sum to 1 Since a Texan can only be male or female (in this context), the sum of the probabilities of selecting a male or a female must equal 1. That is: P ( M ) + P ( F ) = 1
Calculate the probability of selecting a female We can rearrange the equation to solve for the probability of selecting a female, P(F): P ( F ) = 1 − P ( M ) Substituting the given value for P(M): P ( F ) = 1 − 0.4965 P ( F ) = 0.5035
State the final answer Therefore, the probability that a randomly selected Texan in 2000 was female is 0.5035.
Examples
Imagine you are analyzing demographic data for a city and want to determine the gender distribution. If you know the percentage of males in the city, you can easily calculate the percentage of females by subtracting the male percentage from 100%. This simple calculation is crucial for urban planning, resource allocation, and understanding the city's population structure.
