Question

Find the probability that among three random digits, with each digit (0 through 9) being equally likely (so each triple equally likely):

a. All three are alike.

b. No two are alike.

c. The first digit is 0.


d. Exactly two are alike.

Answer 1

a)number of ways to select 3 random digits =10³ (As there are 10 choice for each digits)

P(all three are alike)=P(choosing one out of 10 for each place)=¹⁰C₁/10³ =10/1000=1/100=0.01

b)

P(no two are alike)=10*9*8/10³ =720/1000=0.72

c)P( The first digit is 0 )=P(chooing for next 2 digits)=1*10²/10³ =1/10 =0.1

d)P( Exactly two are alike )=P(choose 1 from 10 and then select 2 out of 3 place for it and then select 2nd dgit) =¹⁰C₁*³C₂*9/10³ =10*3*9/1000=270/1000=0.27