An experiment succeeds twice as often as it fails. The probability that in the next six trials there will be at least four successes, is:

Explanation: Solution Step 1: Find the probability of success ( ) and failure ( ) Let the probability of failure be and the probability of success be . According to the question, the experiment succeeds twice as often as it fails: We know that . Substituting : Therefore, . Step 2: Identify parameters for Binomial Distribution Number of trials ( ) = Probability of success ( ) = Probability of failure ( ) = We need to find the probability of at least four successes ( ): Step 3: Calculate individual probabilities Using the Binomial formula : For : For : For : Step 4: Sum the probabilities Final Answer: The probability is .

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