In the following cross tab or contingency table the favorite sport of 50 university students is cross classified with the gender of the respondent, What is the probability of 1 - P(female or basebal) and 2 - (football/male)
gender-baseball-basketball-football-tot
male 8 10 8 26
female 5 12 7 24
total 13 22 15 50
To find the requested probabilities, we need to calculate the probabilities of the events "female or baseball" and "football/male" separately.
1. Probability of "female or baseball" (1 - P(female or baseball)):
To calculate this probability, we need to add the probabilities of being female and being interested in baseball, and then subtract the probability of being both female and interested in baseball.
- Probability of being female: In the contingency table, we see that there are 24 female students out of a total of 50 students. Therefore, the probability of being female is 24/50.
- Probability of being interested in baseball: According to the table, there are 13 students interested in baseball out of a total of 50 students. Therefore, the probability of being interested in baseball is 13/50.
- Probability of being both female and interested in baseball: From the table, we see that there are 5 females interested in baseball. Therefore, the probability of being both female and interested in baseball is 5/50.
Now we can calculate the probability of "female or baseball" by adding the probabilities of being female and interested in baseball and then subtracting the probability of being both female and interested in baseball:
P(female or baseball) = (24/50) + (13/50) - (5/50)
2. Probability of "football/male":
To calculate this probability, we need to divide the number of males interested in football by the total number of males.
- Number of males interested in football: From the table, we see that there are 8 males interested in football.
- Total number of males: From the table, we see that there are 26 males in total.
Now we can calculate the probability of "football/male" by dividing the number of males interested in football by the total number of males:
P(football/male) = 8/26
Therefore, the requested probabilities are:
1. 1 - P(female or baseball) = 1 - [(24/50) + (13/50) - (5/50)]
2. Football/male = 8/26