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Alevel maths stats question!

This is a question from one of the practice papers, I can’t understand what they’ve done in the mark scheme at all, please could someone explain how to do this? :smile:

The 24 members of staff at the Blackley branch of the Midshires Bank decide to start a lottery.
They will each pay €5 per week to enter the lottery.
Each week, three of the numbers 1, 2, 3 and 4 will be placed in a random order by a computer. Each
member of staff will make 3 different attempts, entered into their computer workstation, to guess
what the computer has chosen.
(a) Show that the probability that a particular member of staff enters the correct numbers in the
correct order in any week is 1/8
You could upload the mark scheme, but
* How many combinations are there?
* How many attempts are made?
Combining those should give the result.

Alternatively do
p(success) = 1 - p(3 successive failures)

Alternately (a bit longer) combine 3 outcomes in a geometric distribution
(edited 1 year ago)
Reply 2
Avatar for Chloe33319
Chloe33319
OP
4
The mark scheme literally just says:

1/24 + 23/24 x 1/23 + 23/24 x 22/23 x 1/22
= 1/8

So do you have to use combinations or something? I’m so confused sorry
Original post by Chloe33319
The mark scheme literally just says:

1/24 + 23/24 x 1/23 + 23/24 x 22/23 x 1/22
= 1/8

So do you have to use combinations or something? I’m so confused sorry

Thats the last way (geometric distribution) so
p(win 1st try) + p(win 2nd try) + p(win 3rd try)
So for instance
p(win 2nd try) = p(win 2nd try | lost 1st try) = p(win 2nd try)p(lose 1st try) = 1/23 * 23/24 = 1/24

The first two ways in the previous post are simpler and give the same result
Reply 4
Avatar for Chloe33319
Chloe33319
OP
4
Ohhh I see thank you!

How would you do it in the simpler way? :smile:
Original post by Chloe33319
Ohhh I see thank you!

How would you do it in the simpler way? :smile:


The first two ways in #2. Have a go and post if you need any help.
The first one should be obvious, and the 2nd one just requires you to model 3 successive failures.

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