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Answer :
Final answer:
To calculate the probability of consecutive wins, we multiply the individual probabilities for each event. The probability of Emerson winning two games in a row is 0.1369, while the probability that Emerson wins five games in a row is 0.0105.
Explanation:
The subject of this question is probability, specifically related to consecutive win scenarios in games. Emerson wins 37% of all checker games, which can be expressed as a probability of 0.37.
(a) To calculate the probability that Emerson wins two games in a row, we multiply the individual probabilities of each game. Thus, 0.37(Emerson winning the first game) x 0.37(Emerson winning the second game) = 0.1369. Hence, the probability that Emerson wins two games in a row is 0.1369 or 13.69%.
(b) Similarly, for calculating for five consecutive wins, we multiply the probability of each game i.e., 0.37 to the power of 5. So, 0.37^5 = 0.0105 (rounded to four decimal places). Therefore, the probability that Emerson wins five games in a row is 0.0105 or 1.05%.
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