Statistics And Probability Question 59
Question: A boy is throwing stones at a target. The probability of hitting the target at any trial is $ \frac{1}{2} $ . The probability of hitting the target 5th time at the 10th throw is:
Options:
A) $ \frac{5}{2^{10}} $
B) $ \frac{63}{2^{9}} $
C) $ \frac{^{10}C_5}{2^{10}} $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
- [b] The probability of hitting the target 5th time at the 10th throw = P (the probability of hitting the target 4 times in the first 9 throws) $ \times $ (the probability of hitting the target at the 10th throw) $ = ^{9}C_4{{( \frac{1}{2} )}^{4}}{{( \frac{1}{2} )}^{5}} =\frac{9!}{4!5!}\times {{( \frac{1}{2} )}^{10}}=\frac{63}{2^{9}} $
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