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Answer:
First we will count the total number of ways in which six numbers can be drawn, and the number of ways the six numbers on the ticket can match the numbers drawn from the machine.
As order does not matter so, the number of possible outcomes of the lottery drawing is :
48C6 = 12,271,512.
Out of these, only one will match all six numbers on the player’s ticket, so the probability of winning the grand prize of $1,000,000 is:
[tex]\frac{6C6}{48C6} =\frac{1}{12271512} =0.000 0000815[/tex]
The probability of the winning prize of $1,000,000 of getting the sixth ticket is 0.0000000815.
What is probability?
Probability means possibility. It deals with the occurrence of a random event. Its basic meaning is something is likely to happen. It is the ratio of the favorable event to the total number of events.
In a certain state’s lottery, 48 balls numbered 1 through 48 are placed in a machine and six of them are drawn at random.
If the six numbers are drawn match the numbers that a player had chosen, the player wins $1,000,000
Then the favorable condition will be
[tex]\rm ^6C_6 = 1[/tex]
And the total event will be
[tex]\rm ^{48} C _6 = \dfrac{48!}{42!*6!}\\\\^{48} C _6 = \dfrac{48*47*46*45*44*43}{6*5*4*3*2}\\\\^{48} C _6 = 12,271,512[/tex]
Then the probability will be
[tex]\rm P = \dfrac{favoeable \ event }{total \ event}\\\\\\P = \dfrac{1}{12,271,512}\\\\\\P = 0.0000000815[/tex]
Thus, the probability is 0.0000000815.
More about the probability link is given below.
https://brainly.com/question/795909
