The digits 0 through 9 are each written on a small wooden tile. The tiles are pu
ID: 3148952 • Letter: T
Question
The digits 0 through 9 are each written on a small wooden tile. The tiles are put into a black bag. Tiles are removed one at a time in sequence, the digit is written down and the tile is returned to the bag.
Example: 1st tile removed is a 6. Replace the tile, shake the bag and pick a tile. 2nd pick is a 0. Replace, shake, and pick. 3rd tile is a 7. So the number picked is 607
If three tiles are picked …
a) What is the probability of producing a number divisible by 5?
b) What is the probability of producing three repeated digits?
c) What is the probability of producing a number without an even digit?
d) What is the probability of producing three distinct digits?
Explanation / Answer
If three tiles are picked …
a) What is the probability of producing a number divisible by 5?
Here as the number could be replaced then total possibilities are = 103 = 1000
Here number of tiles which have a number divisible by 5, so it should end in 0 or 5. so there are 2 out of 10 possibilities.
Pr(Producing number divisble by 5) = 2/10 = 1/5 = 0.2
b) What is the probability of producing three repeated digits?
Answer : Producing three repeated digits. THere are 10 digits so there are 10 such numbers 000,111,222,....999
Pr(Three repeated digits) = 10/1000 = 1/100 = 0.01
c) What is the probability of producing a number without an even digit?
Answer : A number without an even digit, so there are not even digits are 1,3,5,7,9 . Total such digits are 5
Total such possibilities are = 5 * 5 * 5 = 125
So, Pr(all odd digit) = 125/1000 = 1/8 = 0.125
d) What is the probability of producing three distinct digits?
Answer : Total possibilities of three distinct digits = First digit have 10 options , second one 9 options and third one 8 options = 10 * 9 * 8 = 720
Pr(Three districnt digits) = 720/1000 = 0.72