7. In a state lottery, a player must choose 8 of the numbers from 1 to 40. The lottery commission then performs an experiment that selects 8 of these 40 numbers. Assuming that the choice of the lottery commission is equally likely to be any of the 40 8 combinations, what is the probability that a player has (a) all 8 of the numbers selected by the lottery commission

Answer:a) P (8 of the players numbers are drawn) = 1.3*10^-8

b) P (7 of the players number are drrawn) = 3.33*10^-c) P (at least 6 of the players number were drawn) = 1.84*10^-4

Step-by-step explanation:

Players has 8 combinations of numbers from 1-40. The outcome S contains all the combinations of 8 out of 40

a) P (8 of the players numbers are drawn) = 1/40/8 = 1.3*10^-8

There are one in hundred million chances that the draw numbers are precisely the chosen ones.

b) Number of ways of drawing 78 selected numbers from 1-40=8 * (40-7)

8*32

P (7 of the players number are drawn) = 8*32/40 = 3.33*10^-6.

There are approximately 300,000 chances that 7 of the players numbers are chosen

c) P (at least 6 players numbers are drawn) = 32/2 * (8/6) ways to draw.

P (at least 6 players numbers are drawn) = P (all 8 chosen are drawn) + P (7 players numbers drawn) + P (6 chosen are drawn) = 1 + 8 x32/40/8 + [8/6 * 32/2]

P (at least 6 players numbers are drawn) = 1.84*10^-4.

There are approximately 5400chances that at least6 of the numbers drawn are chosen by the player.