A serial number on a 5$ bill includes 3 letters followed 7 digits. Assuming the digits are randomly assigned, what is the probability that the serial number will contain at least five even digits?
+23245 There are 5 even digits and 5 odd digits, so the probability that any digit is even is 5/10 = 1/2 = 0.50.
Similarly, the probability that any digit is odd is 0.50.
This is a binomial distribution. The appropriate formula is: nCr·pr·qn-r
To get exactly 5 even digits:
n = total number of chances = 7
r = total number of successes (getting an even digit) = 5
p = probability of success (getting an even digit) = 0.50
q = probability of failure (getting an odd digit) = 0.50
nCr·pr·qn-r = 7C5·(0.50)5·(0.50)7-5 = 0.0410
To get at least 5 digits, we must find the probability of getting exactly 5, of getting exactly 6, and of getting exactly 7, and adding together these three answers.
We have the answer for exactly 5, we now need the answer for exactly 6, so we need to re-do the above with r being 6, and we also need the answer for exactly 7, so we will also need to re-do the avove with r being 7, and then add these three answers together.
+23245 There are 5 even digits and 5 odd digits, so the probability that any digit is even is 5/10 = 1/2 = 0.50.
Similarly, the probability that any digit is odd is 0.50.
This is a binomial distribution. The appropriate formula is: nCr·pr·qn-r
To get exactly 5 even digits:
n = total number of chances = 7
r = total number of successes (getting an even digit) = 5
p = probability of success (getting an even digit) = 0.50
q = probability of failure (getting an odd digit) = 0.50
nCr·pr·qn-r = 7C5·(0.50)5·(0.50)7-5 = 0.0410
To get at least 5 digits, we must find the probability of getting exactly 5, of getting exactly 6, and of getting exactly 7, and adding together these three answers.
We have the answer for exactly 5, we now need the answer for exactly 6, so we need to re-do the above with r being 6, and we also need the answer for exactly 7, so we will also need to re-do the avove with r being 7, and then add these three answers together.
