A computer generates single-digit random numbers from 0 to 9 inclusive. Each digit is equally likely to be generated. If 50 such digits are generated what are the probabilities of obtaining:
a). 5 or more twos,
b). 4 or less threes,
c). between 6 and 10 (inclusive) sevens?
(0.5688, 0.4312, 0.3745)
The script for the question is straightforward, but the calculation is a bit long. Essentially:
n = number of trials = 50
x = number of successful events (dependent on question)
p = probability of success in one trial = 1/10 for any digit as stated in the question.
Again, the calculation formula is: nCx times P to the power x times (1 - P) to the power( n - x )
Don't know how to superscript on here, so here's a link that explains it well. This is the essential bit.
http://stattrek.com/Lesson2/Binomial.aspxThe nCx is the formula for combinations.
a) 5 or more '2' (5 is inclusive)
The method to calculate would be 1 - p[0 number of '2' + 1 number of '2' + 2 no of '2' + 3 no of '2' + 4 no of 2]
so, 1 - 0.4312 (4 decimal places) = 0.5688
b) The answer's already in 'a' : The calculation in the brackets was for the quantity 4 or less of any digit: 0.4312 (4 decimal places)
c)I did it like this:
P(less than 11 '7') - P(less than 6 '7')
0.9906... - 0.6161...
0.3745 (4 decimal places)
I used the binomial calculator on that site, but a scientific calculator is necessary. Maybe someone else here can provide a simpler way of solving it.