The probability that the randomly selected student is female or Physics major is 0.625.
Given Information
Total number of students = 40
Number of Physics major out of the total students, P = 15
Number of females in the class, F = 16
Number of females that are Physics major, (P∩F) = 6
We have to find the probability P(P∪F).
Calculating the Probability
Probability of Physics major students, P(P) = 15/40
= 0.375
Probability of female students, P(F) = 16/40
= 0.4
Probability of female students who are Physics major, P(P∩F) = 6/40
= 0.15
Since, we know that,
P(P∪F) = P(P) + P(F) - P(P∩F)
∴ P(P∪F) = 0.375 + 0.4 - 0.15
P(P∪F) = 0.625
Thus, the probability that the randomly selected student will be a Physics major or a female is 0.625
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