The digits 0 through 9 are each written on a small wooden tile. The tiles are pu

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

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.