In grade 11 of a school, 40 students opted for Physics, 17 opted for Biology, and 20 opted for Chemistry. If the total number of students in grade 11 was 60, all of these students opted for at least one of the three subjects mentioned here, and exactly five of these students opted for all these three subjects, what is the probability that a randomly selected student of grade 11 of this school would have opted for exactly one of these three subjects?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 0.80
Students opted for Physics = 40
Students opted for Biology = 17
Students opted for Chemistry = 20
The total number of students in grade 11 = 60
Now using Venn diagram -
Total number of students -
a + b + c + d + e + f + 5 = 60
a + b+ c + d + e + f = 55 ...(1
Students who opted for physics -
a + b + f + 5 = 40
a + b + f = 35 ...(2
Students who opted for biology -
b + c + d + 5 = 17
b + c + d = 12 ...(3
Students who opted for chemistry -
d + e + f + 5 = 20
d + e + f = 15 ...(4
Adding eq.(2, (3 and (4 -
a + c + e + 2b + 2d + 2f = 35 + 15 + 12
a + c + e + 2b + 2d + 2f = 62 ....(5
Multiplying eq(1 by 2 -
2a + 2b + 2c + 2d + 2e + 2f = 110 ....(6
Subtracting eq(5 from (6, we get -
a + c + e = 110 - 62 = 48
Probability of the event = Favourable number of outcomes/Total number of outcomes
The probability that a student would have opted for exactly one of these three subjects = 48/60 = 0.80