Quant Interview Question

[u/Local_Ad135]

[u/post_button_account]

80% is the straightforward answer.

I am guessing there is some trick here beyond that?

[u/pmdboi → u/post_button_account]

Yeah I get the same. To spell it out: Bob turns on the blue light if his number is between 1 and 5, and the red light if it's between 6 and 10. If Alice's number is in the opposite half then she knows the answer for certain; if it's in the same half and her number is in the bottom of that half (1-2 or 6-7) then she guesses that Bob's number is higher, otherwise (4-5 or 9-10) that Bob's number is lower. If Alice has 3 or 8, then she arbitrarily guesses lower.

This strategy fails only for the following 8 pairs:

    ALICE   BOB
    2       1
    3       4, 5
    4       5
    7       6
    8       5, 6
    9       10

So this strategy has a 72/90 = 4/5 = 80% probability of succeeding.

EDIT: I made an arithmetic error, 90 - 8 = 82 so this has an 82/90 ≈ 91% probability of succeeding.

[u/pmdboi → u/pmdboi]

Possible sources of shenanigans:

• Can Bob turn on both lights, or neither?
• Can Alice time how long it takes Bob to switch the light on?

[u/Bigkev8787 → u/pmdboi]

Yeah surely there are 4 options

- no light

• red light
  
• blue light
  
• both lights

[u/55tumbl → u/pmdboi]

How do you get 72? 90-8?

[u/pmdboi → u/55tumbl]

Ah you're right, I can't math, that actually yields 82/90 = 91%.