Question

In a class of 100 students, 30 major in Mathematics. Moreover, of the 40 females in the class, 10 major in Mathematics. If a student is selected at random from the class, what is the probability that the student will be a male or will major in Mathematics (or both)?

Answer 1

The probability of male is simple.  M + F = 100 and we know (from the question) that F = 40. So 60 out of 100 students is male, hence the probability of a randomly selected student being male is 60% (0.6).

Likewise, 30 of the 100 are in mathematics, so 30% is the probability.

that 10 of the 40 women are in mathematics, so male in mathematics is 20,

Therefore probablity of both is 20%.

Answer 2

SOLUTION 

Total students = 100

Total major in Mathematics = 30

Female = 40 , Female majors in Mathematics = 10

=> Male = 100 - 40 = 60

=> Male majors in Mathematics = 30 - 10 = 20

So,

P(Male) 

= Males / Total students 

= 60/100 

= 0.60 (ANSWER)

P(Major in Mathematics) 

= Total majors in Mathematics / Total students

= 30/100

= 0.30 (ANSWER)

P(Major in Mathematics and Male)

= Male majors in Mathematics / Males

= 20/60

= 1/3

= 0.33

So,

P(Male or Major in Mathematics) or both

= P(Male) + P(Major in Mathematics) - P(Male and Major in Mathematics)

= 0.60 + 0.30 - 0.33

= 0.57 (ANSWER).