Question

According to a survey conducted by an environmental organization, the probability that an eligible voter cares strongly about environmental issues is 0.63, the probability that an eligible voter votes regularly is 0.51 and the probability that an eligible voter both votes regularly and care strongly about environmental issues is 0.30. If an eligible voter is selected at random what is the probability that the person cares strongly about environmental issues but does not vote regularly

Answer 1

The probability that the person cares strongly about environmental issues but does not vote regularly is P=0.33.

Explanation:

We have:

Probability that the voter cares for the environment P(E)=0.63

Probability that the voter votes regularly P(R)=0.51

Probability that the voter votes regularly and cares for the environment P(R,E)=0.30

We have to calculate the probability that the voter cares for the environment but does not vote regularly P(not R, E).

We know that the probability that the voter cares for the environment is 0.63, and is divided between the ones that vote regularly and the ones that don't:

P(E)=P(R,E)+P(not R,E)=0.63

We also know that the probability that the voter votes regularly and cares for the environment is P(R,E)=0.30. Then:

P(E)=0.30+P(not R,E)=0.63

P(not R,E)=0.63-0.30=0.33

The probability that the person cares strongly about environmental issues but does not vote regularly is P=0.33.