Great Expectations.

Probability Level 2

Krishna throws 6 mangoes into two bins labeled KA and KI , with each mango having an equal probability of landing in either bin.

Radha then chooses the bin with more Mangoes (picking the bin labelled KA if both bins are equally loaded).

If the expected number of mangoes she gets can be expressed as a/b, where and are positive co-prime integers,

Then what is a + b ?


The answer is 79.

Vijay Simha by Vijay Simha , 34, USA

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1 solution

Zee Ell
Nov 3, 2018

( 1 2 ) 6 × ( 6 × ( 6 6 ) × 2 + 5 × ( 6 5 ) × 2 + 4 × ( 6 4 ) × 2 + 3 × ( 6 3 ) × 1 ) = 252 64 = 63 16 (\frac {1}{2})^6 × (6 × {6 \choose 6} × 2 + 5 × {6 \choose 5} × 2 + 4 × {6 \choose 4} × 2 + 3 × {6 \choose 3} × 1) = \frac {252}{64} = \frac {63}{16}

63 + 16 = 79 63 + 16 = \boxed {79}

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