2 In A Row - QuantGuide

Questions Mental Math Discussion Pricing

2 In A Row

Medium

Probability

You have a coin where you can decide the probability

p

of obtaining a heads before flipping the coin

4

times. What value of

p

maximizes the probability that you obtain exactly two consecutive heads in your

4

flips? For example,

HHHT

and

HHHH

are not allowed, but

HHTH

is allowed. The answer is in the form

\dfrac{a-\sqrt{b}}{c}

for integers

a,b,

and

c

with

c

minimal. Find

a + b + c

Notes

Hint

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2 In A Row

Medium

Probability

You have a coin where you can decide the probability

p

of obtaining a heads before flipping the coin

4

times. What value of

p

maximizes the probability that you obtain exactly two consecutive heads in your

4

flips? For example,

HHHT

and

HHHH

are not allowed, but

HHTH

is allowed. The answer is in the form

\dfrac{a-\sqrt{b}}{c}

for integers

a,b,

and

c

with

c

minimal. Find

a + b + c

Notes

Hint