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# A fair coin is tossed 6 times. What is the probability

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A fair coin is tossed 6 times. What is the probability [#permalink]  06 Sep 2019, 11:59
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Question Stats:

28% (02:51) correct 71% (02:48) wrong based on 7 sessions
A fair coin is tossed 6 times. What is the probability of getting no any two heads on consecutive tosses?

A. $$\frac{21}{64}$$

B. $$\frac{42}{64}$$

C. $$\frac{19}{64}$$

D. $$\frac{19}{42}$$

E. $$\frac{31}{64}$$
[Reveal] Spoiler: OA

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Extra: Permutations, and Combination

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Re: A fair coin is tossed 6 times. What is the probability [#permalink]  07 Sep 2019, 09:00
Expert's post
This is a question which is not good or practice. It is too hard for the GRE.
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Re: A fair coin is tossed 6 times. What is the probability [#permalink]  08 Sep 2019, 04:20
Can someone post a mathematical solution to this?
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Re: A fair coin is tossed 6 times. What is the probability [#permalink]  12 Sep 2019, 21:44
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huda wrote:
A fair coin is tossed 6 times. What is the probability of getting no any two heads on consecutive tosses?

A. $$\frac{21}{64}$$

B. $$\frac{42}{64}$$

C. $$\frac{19}{64}$$

D. $$\frac{19}{42}$$

E. $$\frac{31}{64}$$

TTTTTT (1)

TTTTTH (6)

HTHTTT (4+3+2+1)

HTHTHT (2+2)

= 21 ways

2^6 combinations = 64

21/64

I can't think of a faster way off the top of my head
Re: A fair coin is tossed 6 times. What is the probability   [#permalink] 12 Sep 2019, 21:44
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