This applet can be used to explore calculating probabilities for independent events.
e.g. using the default dimensions.
Check the left hand tick box, move the fish into the red zone A. What is the probability of the fish being in area A, P(A)?
By considering the depth
Unchecked the left-hand box and check the top one. What is the probability of the fish being in area B, P(B)?
By considering the width of the tank
Now check the left hand box again. What is the probability of the fish being in region A and B at the same time? This time we need to think about the area.
But it should also be evident that this equivalent to multiplying the fractions. i.e. we want .
This can be followed by a discussion of assumptions, i.e. the events must be independent.
Further problems can be generated by moving the cross-hairs to re-dimension the tank and regions.
There is a worksheet attached that allows students to explore multiplication of probabilities for 'and' probability problems.