In the Daily4 game four numbers between 0 and 9 will be draw

In the Daily4 game, four numbers between 0 and 9 will be drawn in succession (repetitions allowed). The player marks four numbers on a game card and has a choice of how to play, straight (the player’s numbers will match the four numbers drawn in exact order) or box (the player’s numbers will match the four drawn in any order).

a. What is the size of the sample space?

b. What is the probability of a straight?

c. What is the probability of a box if four distinct numbers are drawn?

d. What is the probability of a box if two of the numbers drawn are the same?

e. What is the probability of a box if two distinct pairs of numbers are drawn?

f. What is the probability of a box if three of the numbers drawn are the same?

Solution

a)

size of the sample space = 10*10*10*10 = 10000

b)

probability of a straight

10 P 4 = 5040

5040 / 10,000 = 0.504

c)

10 C 4 = 210

210 / 10,000 = 0.021

d)

10 C 2 = 45

45 / 10,000 =0.0045

e)

10 C 2 * 10 C 2 = 2025

2025 / 10,000 = 0.2025

f)

10 C 3 = 120

120 / 10,000 = 0.012