A school has 500 students

MATHEMATICS · Multi-part · A Level · Mathematics · Probability · Probability

Problem

A school has 500 students. One student is selected at random. The following probabilities are known:

P(L)=0.10

, where

L

: “the student is left-handed”

P(G)=0.20

, where

G

: “the student wears glasses”

P(I)=0.30

, where

I

: “the student plays a musical instrument”

P(L\cap G)=0.02

P(L\cap I)=0.03

P(G\cap I)=0.06

P(L\cap G\cap I)=0.006

. (i) Test whether events

L

and

G

are independent. (ii) Test whether event

I

is independent of

L

and also independent of

G

, stating your reasoning clearly in each case. (iii) Compute

P(G\mid L\cap I)

and interpret its value with reference to independence.