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Question
An experiment succeeds twice as often as it fails. Find the probability that in the next six trials, there will be at least 4 successes.
Solution
The probability of success is twice the probability of failure.
Let the probability of failure be x.
∴ Probability of success = 2x
Let X be the random variable that represents the number of successes in six trials.
By binomial distribution, we obtain
P (X = x) = `""^nC_x P^(n-x) q^x`
Probability of at least 4 successes = P (X ≥ 4)
= P (X = 4) + P (X = 5) + P (X = 6)
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