Number of ways to pick 4 random even digits = 5^4 = 625
Number of ways to pick 4 random digits = 10^4 10000
So prob. of all even = 625/10000 = 1/16
The expected (i.e. most likely) number of even digits is 2. This is because the peak of the binomial distribution occurs for 2 even digits. You have a 4/16 = 1/4 probability of 1 even digit, a 4/16 = 1/4 probability of 3 even digits, a 1/16 probability of no even digits and thus a 6/16 = 3/8 probability of 2 even digits. These numbers come straight from Pascal's triangle 1 4 6 4 1
Paula moves to an area with a different telephone exchange. Telephone numbers in the new exchange start with 753, and all combinations of the four remaining digits are equally likely.
a) Calculate the probability that the last four digits in Paula’s new telephone number are odd digits.
b) What is the expected number of odd digits in her new telephone number?
1 answer