Eventually tossed a coin many times Part-III

Probability Level 3

A fair coin is tossed 10 times. If the probability of getting at most six heads is a b \dfrac{a}{b} , where a a and b b are coprime positive integers, find the value of a + b a+b .


The answer is 117.

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Sandeep Bhardwaj by Sandeep Bhardwaj , 28, India

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3 solutions

Instead of calculating each combination, you can refer to Pascal's Triangle's 10th row.

1 − 10 − 45 − 120 − 210 − 252 − 210 − 120 − 45 − 10 − 1 1-10-45-120-210-252-210-120-45-10-1 The possibility of at least 6 heads will be the sum of the first 7 (including 0 heads) numbers in this row. P < = 6 = 1 + 10 + 45 + 120 + 210 + 252 + 210 2 10 P_{<=6} = \frac{1+10+45+120+210+252+210}{2^{10}} P < = 6 = 848 1024 P_{<=6} = \frac{848}{1024} 53 64 \large \boxed{\frac{53}{64}}

2 Helpful 2 Interesting 0 Brilliant 1 Confused

(10C0+10C1+10C2+10C3+10C4+10C5+10C6)/2^10=53/64=>117

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Deepak Kumar
Apr 2, 2015

(10C0+10C1+10C2+10C3+10C4+10C5+10C6)/2^10=53/64=>117

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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