An unbiased coin is tossed three times

MATHEMATICS · Multi-part · AP · AP Statistics · Probability Random Variables Distributions · Probability Random Variables Distributions

Problem

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. (i) Treating the four outcomes as mutually exclusive and exhaustive, determine the value of

k

. (ii) Using the completed distribution, calculate

P(X\ge 2)

. (iii) Verify that the distribution obtained in part (i) satisfies the axiomatic conditions of probability.