MATHEMATICS · Multi-part · CBSE · Mathematics · Probability · Probability
Problem
Four mutually exclusive and exhaustive outcomes R, S, T and U are observed in a certain industrial quality-check experiment. Their probabilities satisfy the following conditions:
(1) P(R)+P(S)=0.55
(2) P(T)=2P(U)
(3) P(U)=P(R)−0.10
Answer the questions below.
(i) Using the above information, determine P(R), P(S), P(T) and P(U).
(ii) Present the full probability table for the four outcomes and verify that it represents a valid probability distribution.
(iii) Find the probability that either outcome R or outcome T occurs in a single run of the experiment.
(iv) Suppose the experiment is repeated twice independently. Calculate the probability that outcome U occurs at least once in the two runs.