Answer :
Final answer:
The probability that Ari loses two checker games in a row is 11.56%, the probability of losing five in a row is 0.47%, and the probability of losing five in a row but not six is 0.31%. These probabilities are calculated by raising the single event probability to the power of the number of events and multiplying with the probabilities of complementary events.
Explanation:
The subject of this question is probability in mathematics. Given the percentage of games Ari loses, we are asked to calculate the probability of specific sequences of losses.
(a) The probability that Ari loses two checker games in a row would be calculated by multiplying the percentage of one loss by itself i.e., 0.34 * 0.34, that would be 0.1156 or 11.56%.
(b) Similarly, the probability of Ari losing five games in a row would be 0.34^5, which equals 0.0047 or 0.47%.
(c) Now, if we want to know the probability of Ari losing five checker games in a row, but not six, we need to consider that the sixth game is won, thus the formula changes to 0.34^5 * (1-0.34) = 0.0031 or 0.31%. Thus the fact that events are independent implies that their complements are also independent.
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