Answer:
We can use Bayes' theorem to calculate P(R), which states that the probability of an event A given event B is equal to the probability of B given A multiplied by the probability of A, divided by the probability of B:
P(R|T) = P(T|R) * P(R) / P(T)
We can rearrange this equation to solve for P(R):
P(R) = P(R|T) * P(T) / P(T|R)
We are given that P(RI-T) = 0.25, which can be written as:
P(R∩T) = P(R|T) * P(T) = 0.25
We are also given that P(-R|T) = 0.2, which can be written as:
P(-R∩T) = P(-R|T) * P(T) = 0.2 * 0.1 = 0.02
We can use the law of total probability to find P(T|R):
P(T|R) = P(RI-T) / P(R) = 0.25 / P(R)
We can substitute these values into the equation for P(R) to get:
P(R) = P(R|T) * P(T) / P(T|R)
= 0.25 / [P(T|R) * P(T) + P(-R|T) * P(T)]
= 0.25 / [0.25 + 0.02]
= 0.1060
Therefore, the answer is option C: 0.1060.