Tom B.
asked • 07/19/20what are the chances
there are 10 numbers, 1 through 10. Each has a 1 in 10 chance of randomly being selected. What are the chances that one number like 1 is not picked in 23 tries. What is the formula as the number of tries will increase over a period of time.
More
1 Expert Answer
x = number of times a certain number is picked is a binomial variable with a probability (p) of 1/10 = 0.1
so can use binomial formula to figure out how many times a number is picked (x) in a certain number of tries (n), where in this case n = 23, but n could be anything:
P(x, n) = probability picking a number x times in n tries = n!/(x!*n-x!) p^x * (1-p) ^ (n-x)
To figure out probability to not pick 1 in 23 tries is to figure out the probability it is picked no times in 23 tries, so x = 0 and n = 23:
23!
---- 0.1^0 * 0.9^23 = 0.088
0! 23!
Still looking for help? Get the right answer, fast.
Ask a question for free
Get a free answer to a quick problem.
Most questions answered within 4 hours.
OR
Find an Online Tutor Now
Choose an expert and meet online. No packages or subscriptions, pay only for the time you need.
Tom K.
What would have made this a more interesting problem would have been if the number of tries equaled the number of numbers or if it remained a constant multiple of the number of numbers as the chances went to infinity. If there is a problem like this, please post it.07/19/20