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exam in probo

by maihuna » Fri Aug 14, 2009 4:57 am
In an examination, 20 questions of true-false type are asked. Suppose a student tosses a fair coin to determine his answer to each question. If the coin falls heads, he answers 'true'; if it falls tails, he answers 'false'. Find the probability that he answers at least 12 questions correctly.
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by Neo2000 » Fri Aug 14, 2009 9:51 pm
Probability that he will answer TRUE = 1/2
Probability that he will answer FALSE = 1/2

To get atleast 12 right, he must answer at most 8wrong

which means he can get 0wrong, 1wrong, 2wrong...8wrong

Probability of getting 1 wrong = 20C1 (1/2)^(19) x (1/2)^(1)
Probability of getting 2 wrong = 20C2 (1/2)^(18) x (1/2)^(2)
Probability of getting 0 wrong = 20C0 (1/2)^(20) x (1/2) ^(0)
...
...
...
Probability of getting 8 wrong = 20C8 (1/2)^(12) x (1/2)^(8)

Therefore Probability of getting atleast 12 Right = 1 - (Sum of Above)