- Jake and Kamil are sometimes late for school.
The events \(J\) and \(K\) are defined as follows
\(J =\) the event that Jake is late for school
\(K =\) the event that Kamil is late for school
\(\mathrm { P } ( J ) = 0.25 , \mathrm { P } ( J \cap K ) = 0.15\) and \(\mathrm { P } \left( J ^ { \prime } \cap K ^ { \prime } \right) = 0.7\)
On a randomly selected day, find the probability that
- at least one of Jake or Kamil are late for school,
- Kamil is late for school.
Given that Jake is late for school,
- find the probability that Kamil is late.
The teacher suspects that Jake being late for school and Kamil being late for school are linked in some way.
- Determine whether or not \(J\) and \(K\) are statistically independent.
- Comment on the teacher's suspicion in the light of your calculation in (d).