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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. - CBSE (Commerce) Class 12 - Mathematics

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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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Solution 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. Concept: Bernoulli Trials and Binomial Distribution.
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