If the number of trials is 50. Then the probability that he will not roll a 3 on his next roll will be 0.20 or 20 %.
How to find that a given condition can be modeled by binomial distribution?
Binomial distributions consist of n independent Bernoulli trials.
Bernoulli trials are those trials that end up randomly either on success (with probability p) or on failures( with probability 1- p = q (say))
Suppose we have random variable X pertaining to a binomial distribution with parameters n and p, then it is written as
The probability that out of n trials, there'd be x successes is given by
P(X = x) = ⁿCₓ pˣ (1 - p)ⁿ ⁻ ˣ
Sawyer conducted an experiment in which he rolled a number cube 50 times. He rolled the number 3 a total of seven times.
Then the probability that he will not roll a 3 on his next roll will be
p = 1/6 = 0.1667
q = 1 - p = 1 - 1/6 = 0.8333
Then the probability will be
P = ⁵⁰C₇ (0.8333)⁴¹ (0.1667)⁷
P = 0.20
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