What is the value of p+q?
Consider the following for the next two (02) items that follow : An unbiased coin is tossed n times. The probability of getting at least one tail is p and the probability of at least two tails is q and p-q=\frac{5}{32}.
- A. \frac{57}{32} ✓
- B. \frac{53}{32}
- C. \frac{51}{32}
- D. 1
Correct Answer: A. \frac{57}{32}
Explanation
With n=5, we find p = 1 - P(X=0) = 1 - (\frac{1}{2})^5 = 1 - \frac{1}{32} = \frac{31}{32}. Since p - q = \frac{5}{32}, we have q = p - \frac{5}{32} = \frac{31}{32} - \frac{5}{32} = \frac{26}{32}. Their sum is p + q = \frac{31}{32} + \frac{26}{32} = \frac{57}{32}.
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