Question:
The probability that a bomb will hit the target is \(0.8\). Out of 6 bombs dropped, probability that at least 1 will miss the target is...
The probability that a bomb will hit the target is \(0.8\). Out of 6 bombs dropped, probability that at least 1 will miss the target is...
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At least one miss is the complement of all six bombs hitting.
Updated On: Oct 1, 2026
- \((\frac{1}{5})^6\)
- \(1-(\frac{1}{5})^6\)
- \((\frac{4}{5})^6\)
- \(1-(\frac{4}{5})^6\)
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The Correct Option is D
Solution and Explanation
Step 1: Understand the concept
The bombs are independent. "At least 1 will miss" is the complement of "all 6 hit the target".
Step 2: Probability of all hits
\(P(\text{hit}) = 0.8 = \frac{4}{5}\), so \(P(\text{all 6 hit}) = \left(\frac{4}{5}\right)^6\).
Step 3: Use the complement
\[ P(\text{at least 1 miss}) = 1 - \left(\frac{4}{5}\right)^6 \]
Step 4: Check the options
\(\left(\frac{1}{5}\right)^6\) is the probability that all six miss, which is different from at least one missing. \(\left(\frac{4}{5}\right)^6\) is the probability of all hits. The correct choice is option (D).
Final Answer:
The probability is 1 - (4/5)^6. This is option (D). \[ \boxed{\text{(D) }1-\left(\frac{4}{5}\right)^6} \]
The bombs are independent. "At least 1 will miss" is the complement of "all 6 hit the target".
Step 2: Probability of all hits
\(P(\text{hit}) = 0.8 = \frac{4}{5}\), so \(P(\text{all 6 hit}) = \left(\frac{4}{5}\right)^6\).
Step 3: Use the complement
\[ P(\text{at least 1 miss}) = 1 - \left(\frac{4}{5}\right)^6 \]
Step 4: Check the options
\(\left(\frac{1}{5}\right)^6\) is the probability that all six miss, which is different from at least one missing. \(\left(\frac{4}{5}\right)^6\) is the probability of all hits. The correct choice is option (D).
Final Answer:
The probability is 1 - (4/5)^6. This is option (D). \[ \boxed{\text{(D) }1-\left(\frac{4}{5}\right)^6} \]
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