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प्रश्न
The probability of guessing correctly at least 8 out of 10 answers on a true-false type-examination is ______.
विकल्प
`7/64`
`7/128`
`45/1024`
`7/41`
उत्तर
The probability of guessing correctly at least 8 out of 10 answers on a true-false type-examination is `7/128`.
Explanation:
Here, n = 10
p = `1/2` and q = `1/2` ....(For true/false questions)
And r ≥ 8 i.e. 8, 9, 10
∴ P(X ≥ 8) = P(x = 8) + P(x = 9) + P(x = 10)
= `""^10"C"_8 (1/2)^8 (1/2)^2 + ""^10"C"_9 (1/2)^9 (1/2) + ""^10"C"_10 (1/2)^10 (1/2)^0`
= `45*(1/2)^10 + 10*(1/2)^10 + (1/2)^10 + (1/2)^10`
= `(1/2)^10` (45 + 10 + 1)
= `56 xx 1/1024`
= `7/128`
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