Question

In a high school graduating class of 100 students,54 studied mathematics, 69 studied history, and 35 studied both mathematics and history. If one of these students is selected at random, find the probability that (a) the student took mathematics or history;

Answer 1

Answer :-

22 / 25 or 0.88

Solution :-

Number of students studied mathematics n( M ) = 54

Number of students studied history n( H ) = 69

Number of students studind both history and mathematics n( M ⋂ H ) = 35

Number of students studied history or mathematics n( M ⋃ H ) = ?

Using relation :-

⇒ n( M ⋃ H ) = n( M ) + n( H ) - n( M ⋂ H )

= 54 + 69 - 35

= 123 - 35

= 88

Let the event ' A ' be " Student took mathematics or history"

Number of possible outcomes = Total no. of students = 100

Number of favourable outcomes = 88

Probability of event A = P( A ) = no. of favourable outcomes/ no. of possible outcomes

= 88 / 100

= 22 / 25

Therefore, the probability is 22 / 25 or 0.88.