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Answer :
Final answer:
The probability that Nate wins two games in a row is 13.69%, for five games in a row is 0.416149%, and for winning five games but losing the sixth is 0.262174%.
Explanation:
The subject matter of this question is related to the concept of probability in Mathematics, specifically the probability of independent events. Nate's chances of winning two successive checker games would be the product of his chances of winning each game separately. Nate's winning probability is 37%, or 0.37 in decimal form. Therefore:
(a) The probability that Nate wins two games in a row will be (0.37) * (0.37) = 0.1369 or 13.69%.
(b) Similarly, the probability that Nate wins five games in a row will be (0.37)^5 = 0.00416149 or 0.416149%.
(c) The probability that he wins five games in a row but loses the sixth would be the product of the probability that he wins five games and the probability that he loses one game. The probability of losing one game is 1-0.37=0.63, so the probability is (0.37)^5 * 0.63 = 0.00262174 or approximately 0.262174%.
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