A college has 80 students in Year 12 - Edexcel - A-Level Maths Statistics - Question 3 - 2015 - Paper 1

To find the probability that a student studies Chemistry but not Biology or Physics, we look at those who study only Chemistry.

1. The number of students who study only Chemistry = 7.
2. Total number of students = 80.

The probability is given by: $P( ext{Chemistry only}) = \frac{7}{80} = 0.0875$

1. To find the total number of students studying Chemistry or Physics, we sum up the individual counts, correcting for overlaps:

   • Students studying Chemistry (28) + Students studying Physics (30) - Students studying both (11) = 47.

2. Total probability: $P( ext{Chemistry or Physics}) = \frac{47}{80} = 0.5875$

1. The total number of students studying Biology is 20.
2. Students not studying Biology = Total students - Students studying Biology = 80 - 20 = 60.

The probability is given by: $P( ext{Not Biology}) = \frac{60}{80} = 0.75$

1. Define the probabilities:

   • Let A be the event of studying Biology and B the event of studying Chemistry.
   • P(A) = \frac{20}{80} = 0.25
   • P(B) = \frac{28}{80} = 0.35
   • P(A \cap B) = \frac{7}{80} = 0.0875.

2. Check independence:

   • If A and B are independent, then: $P(A \cap B) = P(A) \cdot P(B)$
   • Calculate: $P(A) \cdot P(B) = 0.25 \cdot 0.35 = 0.0875$

3. Since both values are equal, we conclude that studying Biology and Chemistry are statistically independent.