Question

The Pick 4 games in many state lotteries announce a four‑digit winning number each day. Each of the 10,000 possible numbers 0000 to 9999 has the same chance of winning. You win if your choice matches the winning digits. Suppose your chosen number is 3079 .

(a) What is the probability that the winning number matches your number exactly?

(Enter your answer rounded to four decimal places.)

=
(b) What is the probability that the winning number has the same digits as your number in any order?

(Enter your answer rounded to four decimal places.)

Answer 1

Answer:

a) P(a)= 0.0001

b) P(b)= 0.0024

Step-by-step explanation:

Given:

Chosen number = 3079

Possible numbers that have chance of winning from 0000 to 9999= 10,000

Winning condition=  if made choice matches the winning digits

Now

a)What is the probability that the winning number matches your number exactly?

From 0000 to 9999, only one time can the number 3079 can be the winning number, so

P(a)= 1/10000

     = 0.0001

b)What is the probability that the winning number has the same digits as your number in any order?

Winning numbers from 0000 to 10000 that have same digits as 3079 are

4 x 3 x 2 x 1 = 24 ways

Following are the 24 numbers from 0000 to 9999 that have matching digits to 3079:

0379

0397

0973

0937

0793

0739

3079

3097

3970

3907

3790

3709

7039

7093

7930

7903

7390

7309

9073

9037

9370

9307

9730

9703

P(b)= 24/10000

     =0.0024 !