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secondary 4 | E Maths

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Pls help for q4!

First attempt

-------Pass

------/

-----/

----/

---/ 3/5

--/

-/

Test

-\

--\

---\

----\ 2/5

-----\□□□□□□□second attempt

------\

-------\

--------\-----------------Pass

---------\--------------/

-----------\----------/ 3/5

------------\-------/

------------- Fail

-----------------\

-------------------\ 2/5

---------------------\

-----------------------Fail

The phrasing is odd so here are two solutions :

Interpretation 1 : taking it to mean passing on the 2nd attempt

Probability of failing = 1 - 3/5 = 2/5

Probability of getting a certificate on first 2 attempts

= Probability of failing first attempt x probability of passing second attempt

= 2/5 x 3/5

= 6/25

Interpretation 2 : taking it to mean passing on either the 1st or 2nd attempt.

Probability of failing = 1 - 3/5 = 2/5

Probability of getting a certificate on 2nd attempt

= Probability of failing first attempt x probability of passing second attempt

= 2/5 x 3/5

= 6/25

Probability of getting a certificate on first attempt = 3/5

Total probability

= 3/5 + 6/25

= 15/25 + 6/25

= 21/25

Interpretation 1 :

The 3 participants took 2 attempts each but only 1 made it by the second attempt.

That means the other 2 failed both attempts.

For the two that failed, probability of failing both = 2/5 x 2/5 = 4/25

For the one that passed, the probability

= 6/25 (same as part b 1st interpretation)

Required Probability

= 3 x 4/25 x 4/25 x 6/25

= 288/15625

(Multiplying by 3 is needed as you could have the following situations :

Student 1 passes , other 2 fails

Student 2 passes , other 2 fails

Student 3 passes , other 2 fails

Interpretation 2 :

Includes the above probability and a second case where only one gets a cert but on the first attempt.

For this second case,

For the two that failed, probability of failing both = 2/5 x 2/5 = 4/25

For the one that passed, the probability

= 3/5

Probability for this case

= 3 x 4/25 x 4/25 x 3/5

= 144/3125

Required probability

= 288/15625 + 144/3125

= 288/15625 + 720/15625

= 1008/15625

Passing one of the first n attempts means that n attempts actually have to be made. If not the person would have already attained the cert earlier.

This means the first (n - 1) attempts were fails and the last is a pass.

If we fail once, it's 2/5 x 3/5

If we fail twice, it's 2/5 x 2/5 x 3/5

= (2/5)² x 3/5

If we fail thrice it's 2/5 x 2/5 x 2/5 x 3/5

= (2/5)³ x 3/5

So for failing (n - 1) times , we end up having 2/5 to the power of (n - 1).

Required probability

= (2/5)ⁿ‾¹ x (3/5)

= (3/5)(2/5)ⁿ‾¹

Maybe you are right, it could have meant “on the second attempt”.

The phrasing of the question appears misleading.

Chelsea, follow J’s solutions for this question. I have removed my solutions accordingly.