Respuesta :
Answer:
a) 1/120
b) 1/ 1000
c) 1/720
Step-by-step explanation
a) We have 10 numbers and combinations of 10 elements taking in group of three is:
V₁₀,₃ = 10! /3! ( 10 - 3 ) ! V₁₀,₃ = 10*9*8/6 V₁₀,₃ = 720/6
V₁₀,₃ = 120
So total number of outcomes is 120 therefore the probability of winning is 1 /120
b) Now if numbers can be repeated
each time we pick up one number its probability is 1/10 then for winning the lottery we will have to get:
1/10*1/10+1/10 = 1 / 1000
c) If additionaly to case a) above we need to match the order then
C₁₀,₃ = 10! / ( 10- 3 ) ! ⇒ C₁₀,₃ = 10*9*8 ⇒ C₁₀,₃ = 720
C₁₀,₃ = 720 then the probability of winning is
1/720
By finding the numbers of combinations, we will see that:
- a) P = 1/120
- b) P = 6/1000
- c) P = 1/1000
How to get the probabilities?
The probability will be given by 1 over the total number of possible combinations.
a) If the numbers cannot be repeated, then the total number of combinations is given by:
- For the first number, there are 10 options.
- For the second number, there are 9 options.
- For the third number, there are 8 options.
The number of combinations is given by the product between the numbers of options:
c = 10*9*8 = 720
Then the probability of winning in this case is:
P = 1/720
But the order of the numbers does not matter, so we multiply by the permutations of the 3 numbers = 3! = 3*2 = 6
P = 6/720 = 1/120
b) If the numbers can be repeated, then we have 10 options for the 3 numbers, and the number of combinations is given by:
C = 10*10*10 = 1000
Then the probability is:
P =1/1000
Again, here the order does not matter, so we have:
P = 6/1000
c) Now the order does matter, so this time the probability is just:
P = 1/1000.
If you want to learn more about probabilities, you can read:
https://brainly.com/question/251701
