When a fair coin is tossed 6 times, what is the probability that less

Question

When a fair coin is tossed 6 times, what is the probability that less than 5 heads are tossed?

A. 7/64
B. 5/16
C. 2/3
D. 49/64
E. 57/64

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Mohammadmo · Answer

1- (6C6×1/2^6 + 6C5×1/2^5 ×1/2)= 1-(1/64 +6/64)=57/64

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Himanshu453 · Answer

count the prob of getting all head and 5 heads out of 6,

use combination 6C6 + 6C5 = 7,
total outcomes= 2^6= 64
favorable 64-7= 57
P=57/64

satya2029 · Answer

5H 1T( !6/!5*!1) or 6H(!6/!6)
Total cases= 6+1=7
P(not required)=7/64
P(required)=1-7/64
=57/64
E:)

Archit3110 · Answer

P of atleast 5tails = 6c6*(1/2)^6 + 6c5*(1/2)^6 ; (1/64+6/64) ; 7/64
P of Heads<5 ; 1-7/64 ; 57/64
IMO E

BrushMyQuant · Answer

We need to find When a fair coin is tossed 6 times, what is the probability that less than 5 heads are tossed?

Coin is tossed 6 times => Total number of cases =  2^6  = 64

P(Less than 5 heads) = 1 - (P(5H) - P(6H)

P(5H)

Cases in which we get 5H is same as getting 1 Tail and this can be found by putting 1 tail in any of the 6 slots _ _ _ _ _ _ _ 
This can be done in 6 ways by putting T in any of the 6 slots => 6 ways

=> P(5H) =  \frac{6}{64}

P(6H)

This can be done in 1 way (HHHHHH)

=> P(6H) =  \frac{1}{64}

P(Less than 5 heads) = 1 - (P(5H) - P(6H)  = 1 -  \frac{6}{64}  -  \frac{1}{64}  =  \frac{64 - 7}{64}  =  \frac{57}{64}

So,  Answer will be E 
Hope it helps!

Watch the following video to learn How to Solve Probability with Coin Toss Problems

https://www.youtube.com/watch?v=LRURv38kZw8

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When a fair coin is tossed 6 times, what is the probability that less

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When a fair coin is tossed 6 times, what is the probability that less

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