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Answer :
Final answer:
Dan's probability of losing two checker games in a row is 9%, calculated by multiplying the individual probabilities of losing each game (30% for each game).
Explanation:
The student is asking about the probability that Dan loses two checker games in a row, given that he loses 30% of all checker games he plays. To calculate this, we use the rule of multiplication for independent events.
Let's denote the probability of losing one game as p, which is 0.30 or 30%. Since the games are independent, the probability of losing two games in a row is p multiplied by itself (p imes p). Thus, the probability is 0.30 imes 0.30, which equals 0.09 or 9%.
The calculation is straightforward:
- Probability that Dan loses the first game = 0.30
- Probability that Dan loses the second game = 0.30
- Probability that Dan loses both games in a row = 0.30 imes 0.30 = 0.09 or 9%
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