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Answer: 0.00137
## Explanation Given: - Probability of closing higher = 1/3 - Days are independent - We need probability of 6 consecutive higher closes Since the days are independent, we can multiply the individual probabilities: \[P(\text{6 consecutive highs}) = \left(\frac{1}{3}\right)^6 = \frac{1}{729}\] Now calculate the decimal value: \[\frac{1}{729} \approx 0.001371742\] Comparing with the options: - A: 0.17 (too high) - B: 0.0137 (10 times higher than correct) - C: 0.03704 (27 times higher than correct) - D: 0.00137 (matches our calculation) Therefore, the correct answer is **D. 0.00137** **Key Concept**: When events are independent, the probability of multiple events occurring consecutively is the product of their individual probabilities.
Author: Tanishq Prabhu
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An empirical study of ABC stock listed on the New York Exchange reveals that the stock has closed higher on one-third of all days in the past few months. Given that up and down days are independent, determine the probability of ABC stock closing higher for six consecutive days.
A
0.17
B
0.0137
C
0.03704
D
0.00137