In the pick-4 lottery, 4 digits are drawn randomly in order (drawing 1355 is not the same as drawing 1535). You buy one ticket. Determine the probability that:

Question

a. You win the jackpot.

b. All but your first digit matches the winning four digit number.

c. Exactly three of your four digits matches those of the winning four digit number.

d. At least three of your four digits match those of the winning four digit number.

Answer 1

The sample space consists of all tickets with numbers from 0000 to 9999. There are 10,000 of them.

 

a) 1/10,000

 

b) First digit can be any of 9 numbers:  9/10,000

 

c) Exactly three matches = first or second or third or fourth digit can be any of 9 numbers: 4*(9/10000) =36/10,000

 

d) At least three matches = exactly three or exactly four: (36+1)/10,000=37/10,000

Answer 2

a) Probability one out of ten (0,1,2,...,9): 1/10 = 0.1

   Four times independently: (1/10)·(1/10)·(1/10)·(1/10) = 0.0001

b) Probability of incorrect digit: 9/10

   Probability of correct digit: 1/10

   (9/10)·(1/10)·(1/10)·(1/10) = 0.0009

c) Probability of one incorrect digit is b) times four, because the incorrect digit can be in any one of four places.

   0.0009 · 4 = 0.0036

d) At least three of four =Probability[one incorrect digit] + probability[all digits correct]

   0.0036 + 0.0001 = 0.0037