An unbiased coin is tossed three times. Let the random variable X denote the number of heads obtained. A student begins to complete the probability distribution of X and records the following entries:
Values of X : 0 1 2 3
P(X=x) : 0.10 0.30 k 0.10
Answer the following questions.
a. (i) Treating the four outcomes as mutually exclusive and exhaustive, determine the value of k.
b. (ii) Using the completed distribution, calculate P(X≥2).
c. (iii) Verify that the distribution obtained in part (i) satisfies the axiomatic conditions of probability.