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Carlos scores on each attempt with probability 0.65 and on both with probability 0.585. Are the two attempts independent?
ANo, because 0.585 is not 0.65 times 0.65
BYes, because 0.585 is not 0.65 times 0.65
CNo, because 0.585 is larger than 0.65 itself
DYes, because 0.585 lies between 0 and 0.65
Answer & Solution
Correct answer: A. No, because 0.585 is not 0.65 times 0.65
1. The product of the two separate probabilities is 0.65 times 0.65, which is 0.4225.
2. The actual joint probability is 0.585, which is larger than that product.
3. Since the two numbers differ, the attempts are not independent.
4. That fits the description of a player who shoots in streaks, because scoring first lifts his chance of scoring again to 0.90.
_Source: OpenStax Introductory Business Statistics (CC BY 4.0), Ch 3 "Probability Topics", section 3.3 Two Basic Rules of Probability_
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