$5.$ Let L be the event that a certain lecturer will be lecturing on a particular afternoon and T

the event that he$/$she will be at a doing a Tutorial. Suppose P$($L$)=0\mathrm{.}6$ and P$($T$)=0\mathrm{.}3.$ The

probability that lecturer will be lecturing and doing the tutorial on the same afternoon is $0\mathrm{.}1.$

Determine the following probabilities:

$5\mathrm{.}1$ a lecturer will do at least one of lecturing or tutorial

$5\mathrm{.}2$ a lecturer is not lecturing

$5\mathrm{.}3$ a lecturer is lecturing but not doing the tutorial

$5\mathrm{.}4$ none of the activities are taking place

$5\mathrm{.}5$ Only one activity is taking place