(1 point) In the following problem try to get number answers. Since the numbers
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(1 point) In the following problem try to get number answers. Since the numbers may be qu quite close to zero, you might need to use scientific notation such as 2.3E7 to mean 2.3·1017 23000000 or 5.62E-8 to mean 5.62 & 10"(-8) = 0000000562 In a certain lottery, a computer randomly picks 10 distinct secret numbers from the first 74 positive integers. A player of the lottery has to select 8 numbers If all 8 of them are among the secret numbers, the player wins the grand prize a) From the point of view of the computer that selected the 10 secret numbers, If thte player wins the grand prize, all of the players chosen numbers are in that set of secret numbers. That leaves 2 secret numbers that were not chosen by the player. In how many ways could those 2 secret numbers have been chosen by the computer? b) Comparing the answer from part a to the total number of ways in which the computer could have chosen the 10 secret numbers. you can find the probabililty of the player winning the grand prize That gives a probability ofExplanation / Answer
a)
Two secret numbers which are not in the list of player has to be from the list of 66 remaining numbers.
2 numbers from 66 numbers can be selected in 66C2 ways
= 2145
b)
Total possible combination of selecting 8 numbers from a list of 74 numbers is 74C8 ways.
If a player wins, the selected number has to be 8 among the 10 selected by computer. This can be done in 10C8 ways
Required probability = 10C8/74C8 = 45/1.51E+10 = 2.99E-09
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