In a survey of 400 students in a school, 100 were listed as taking app

1.	In a survey of 400 students in a school, 100 were listed as taking apple juice, 150 as taking orange juice and 75 were listed as taking both apple as well as orange juice. Find how many students were taking neither apple juice nor orange juice.
Answer» Let A – Apple juice; O – Orange juice be the sets. Given; n(U) = 400; n(A) = 100; n(O) = 150; n(A ∩ O) = 75 n (neither apple juice nor orange juice) = n(A’ ∩ O’) = n((A ∪ O)’) = n(U) – n(A ∪ O) = 400 – [n(A) + n(O) – n(A ∩ O)] = 400 – [100 + 150 – 75] = 400 – 175 = 225.

In a survey of 400 students in a school, 100 were listed as taking apple juice, 150 as taking orange juice and 75 were listed as taking both apple as well as orange juice. Find how many students were taking neither apple juice nor orange juice.

Answer»

Let A – Apple juice; O – Orange juice be the sets.

Given; n(U) = 400; n(A) = 100;

n(O) = 150; n(A ∩ O) = 75

n (neither apple juice nor orange juice)

= n(A’ ∩ O’) = n((A ∪ O)’)

= n(U) – n(A ∪ O)

= 400 – [n(A) + n(O) – n(A ∩ O)]

= 400 – [100 + 150 – 75]

= 400 – 175 = 225.