Answer :

Let p be the probability of success in the experiment. Then, q is the probability of failure in the experiment.


According to the question,


An experiment succeeds twice as often as it fails.


p = 2q


But p + q = 1


2q + q = 1 [ p = 2q]


3q = 1



Then, p = 2q




Let X be a random variable representing the number of successes out of 6 experiments.


Then, the probability of getting r success out of n experiments is given by,


P (X = r) = nCrprqn-r


Here, n = 6,



&


…(i)


Then, probability that there will be at least 4 successes out of 6 is given by,


Probability = P (X = 4) + P (X = 5) + P (X = 6)


Put r = 4, 5 and 6 respectively for P (X = 4), P (X = 5) and P (X = 6) in equation (i), we have











Probability = 0.68


, the required probability that in the next 6 trials there will be at least 4 successes is 0.68.


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