Question

32 students were asked which of the sciences they enjoy the most. 4 of the boys said they enjoy Physics. The ratio between boys and girls is 1 : 1 . The probability of picking a girl at random who enjoys Chemistry is 0.25 . Twice as many of the boys said they enjoy Chemistry compared to the girls. The ratio of students who said they enjoyed Physics, Biology and Chemistry was 5 : 5 : 6 respectively.

Answer 1

Step-by-step explanation: Total number of students = 32

Total number of ratio of students that enjoy Physics, Biology and Chemistry = 5 + 5 + 6 = 16

Number of boys that enjoy the three subjects = 16

Number of girls that enjoy the three subjects = 16

Number of students that enjoy Physics = 5/16 X 32 = 10

Number of students that enjoy Biology = 5/16 X 32 = 10

Number of students that enjoy Chemistry = 6/16 X 32 = 12

If number of boys that enjoy Physics = 4

∴ Number of girls that enjoy Physics = 10 - 4 = 6

The probability of girls that enjoy Chemistry = 0.25 = 1/4

∴ The number of girls that enjoy Chemistry = 1/4 X 12 = 3

Hence, the number of boys that enjoy Chemistry = 12 - 3 = 9

Number of boys that enjoy Biology = 9 + 4 - 10 = 13 - 10 = 3

∴ Number of girls that enjoy Biology = 10 - 3 = 7