In: Statistics and Probability
Suppose Emerson loses 30% of all staring contests.
(a) What is the probability that
Emerson loses two staring contests in a row?
(b) What is the probability that
Emerson loses three staring contests in a row?
(c) When events are independent, their complements are independent as well. Use this result to determine the probability that
Emerson loses three staring contests in a row, but does not lose four in a row.
(a)
Probability that Emerson loses staring contests = 0.3
Probability that Emerson loses two staring contests in a row = Probability that Emerson loses in first staring contest * Probability that Emerson loses in second staring contest
= 0.3 * 0.3 = 0.09
(b)
Probability that Emerson loses three staring contests in a row = Probability that Emerson loses in first staring contest * Probability that Emerson loses in second staring contest * Probability that Emerson loses in third staring contest
= 0.3 * 0.3 * 0.3 = 0.027
(c)
Probability that Emerson loses three staring contests in a row = Probability that Emerson loses in first staring contest * Probability that Emerson loses in second staring contest * Probability that Emerson loses in third staring contest * Probability that Emerson wins in fourth staring contest
+
Probability that Emerson wins in first staring contest * Probability that Emerson loses in second staring contest * Probability that Emerson loses in third staring contest * Probability that Emerson loses in fourth staring contest
= 0.3 * 0.3 * 0.3 * (1 - 0.3) + (1 - 0.3) * 0.3 * 0.3 * 0.3
= 0.0189 + 0.0189
= 0.0378