STEP I 1997 question 13 solution - The Student Room
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STEP I 1997 question 13 solution

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Probability for Mr's to plant the traps: Mr1 = 1/10, Mr2 = 2/10, Mr3 = 3/10, Mr4 = 4/10

The probabilities for the vicious attack canary can be disregarded as we get to know that Mr Blond hear it isn't such a thing in the room...

Probability for anaconda being at present: Mr1 = 2/7, Mr2 = 3/7, Mr3 = 4/7, Mr4 = 5/7

Probability for bomb being at present: Mr1 = 1/7, Mr2 = 2/7, Mr3 = 3/7, Mr4 = 4/7


Probability for placements of bombs: Mr1 = (1/10)(1/7), Mr2 = (2/10)(2/7), Mr3 = (3/10)(3/7), Mr4 = (4/10)(4/7)

Total probability of there being a bomb \displaystyle  \frac{1+2^2+3^2+4^2}{70} = \frac{3}{7}

Probability for placements of anacondas: Mr1 = (1/10)(2/7), Mr2 = (2/10)(3/7), Mr3 = (3/10)(4/7), Mr4 = (4/10)(5/7)

Total probability of there being an anaconda \displaystyle  \frac{2+6+12+20}{70}=\frac{4}{7}

Now Mr Blond has two choices, turn on the light or let it be turned off... Probability of ending up dead by chosing:

Turning it on: (4/7)(1/3) by anaconda, (3/7)(1/2) by bomb, Total: \displaystyle \frac{17}{42}

Leaving it turned off: (4/7)(1/2) by anaconda, (3/7)0 by bomb, Total: \displaystyle \frac{12}{42}

This means that the probability of dying is higher if Mr Blond turns the light on, hence he should leave it off.


Solution by nota bene

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