JEE Mains · Maths · STD 11 - 14. probability
An unbiased coin is tossed eight times. The probability of obtaining at least one head and at least one tail is
- A \(\frac{{255}}{{256}}\)
- B \(\frac{{127}}{{128}}\)
- C \(\frac{{63}}{{64}}\)
- D \(\frac{1}{2}\)
Answer & Solution
Correct Answer
(B) \(\frac{{127}}{{128}}\)
Step-by-step Solution
Detailed explanation
Required probability \(=1-\{\mathrm{P}(\text { All Head })+\mathrm{P}\) (All Tail) \({=1-\left\{\frac{1}{2^{8}}+\frac{1}{2^{8}}\right\}} \) \({=1-\left\{\frac{1}{2^{7}}\right\}} \) \({=1-\left\{\frac{1}{128}\right\}=\frac{127}{128}}\)
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