Question

Sawyer conducted an experiment in which he rolled a number cube 50 times. He rolled the number 3 a total of seven times. Based on these results, what is the probability that he will not roll a 3 on his next roll?

Answer 1

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

Learn more about binomial distribution here:

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