3. The following table gives a two-way classification of all basketball players at a university who began their college careers between 2004 and 2008, based on gender and whether or nor they graduated.
Graduated Did Not Graduate
Male 126 55
Female 133 32
a) P(female or did not graduate)
b) P(graduated or male)
There were 181 males and 165 females, making 346 students in all
Of those, 165+55=220 were female or did not graduate
259+55=314 graduated or were male
So,
P(F|~g) = 220/346
P(g|M) = 314/346
To calculate the probabilities in this two-way classification table, you need to understand the basic concepts of probability and how to combine the probabilities.
a) To calculate P(female or did not graduate), you need to calculate the probability of a female and the probability of not graduating, and then add them.
The probability of being a female is represented by the ratio of the number of females to the total number of players:
P(female) = Number of female players / Total number of players
In this case, the number of female players is 133, and the total number of players can be found by adding the number of male and female players: 133 + 126 + 55 + 32 = 346.
So, P(female) = 133 / 346.
Next, you need to calculate the probability of not graduating. In this case, it is represented by the ratio of the number of players who did not graduate to the total number of players:
P(did not graduate) = Number of players who did not graduate / Total number of players
The number of players who did not graduate is given as 55 for males and 32 for females. So, the total number of players who did not graduate is 55 + 32 = 87.
Therefore, P(did not graduate) = 87 / 346.
Now, to calculate P(female or did not graduate), you need to add these probabilities together:
P(female or did not graduate) = P(female) + P(did not graduate)
Substituting the values we calculated, we get:
P(female or did not graduate) = (133 / 346) + (87 / 346)
b) To calculate P(graduated or male), you can follow the same steps as above:
P(graduated) = Number of players who graduated / Total number of players
The number of players who graduated is given as 126 for males and 133 for females. So, the total number of players who graduated is 126 + 133 = 259.
Therefore, P(graduated) = 259 / 346.
Next, you need to calculate the probability of being a male:
P(male) = Number of male players / Total number of players
The number of male players is given as 126, so P(male) = 126 / 346.
Now, to calculate P(graduated or male), you need to add these probabilities together:
P(graduated or male) = P(graduated) + P(male)
Substituting the values we calculated, we get:
P(graduated or male) = (259 / 346) + (126 / 346)
To find the probability of events (a) and (b), we first need to determine the total number of basketball players in each category.
Total number of males: 126 + 55 = 181
Total number of females: 133 + 32 = 165
Total number of players who graduated: 126 + 133 = 259
Total number of players who did not graduate: 55 + 32 = 87
a) P(female or did not graduate) = (Number of females + Number who did not graduate) / Total number of players
= (165 + 87) / (181 + 165)
= 252 / 346
= 0.727
b) P(graduated or male) = (Number who graduated + Number of males) / Total number of players
= (259 + 181) / (259 + 181 + 87 + 32)
= 440 / 559
= 0.787