If a fair coin is tossed 4 times, what's the probability that at least

Question

If a fair coin is tossed 4 times, what's the probability that at least 3 of the 4 tosses will come up heads?

A. 1/16
B. 1/4
C. 5/16
D. 7/16
E. 11/16

eswarchethu135 · Answer

At least 3 of the 4 outcomes will be heads.
Two possible cases: 3 outcomes are heads + 4 outcomes are heads

The 3 outcomes can be selected in  4_C_3  ways. So  4_C_3 * (\frac{1}{2})^4

=  (\frac{1}{2})^2

All 4 can be heads. =  (\frac{1}{2})^4

=  (\frac{1}{4})  +  (\frac{1}{16})

=  \frac{5}{16}

OPTION:  C

gadde22 · Answer

Total number of outcomes for tossing a coin for 4 times is 2*4 = 16

Number of ways to get at least 3 heads = now of ways to get 3 heads + now of ways to get 4 = 4 + 1=

So probability = 5/16 and the answer is C

Archit3110 · Answer

For 4 tosses P of getting exactly heads = (1/2)^4= 1/16
P of getting exactly 3 heads and 1 tail= 4c3* (1/2)^4= 1/4

1/16+1/4= 5/16 option C

BrushMyQuant · Answer

Given that a fair coin is tossed 4 times, and we need to find what's the probability that at least 3 of the 4 tosses will come up heads?

Coin is flipped 4 times => Total number of cases =  2^4  = 16

At least 3 heads means that we can get 3 or more heads.

=>  P(At least 3 heads) = (Cases in which we get 3 or 4 Heads) / 16

Cases in which we will get 3H

Case in which we get 3 heads are same as the cases in which we get 1T. We can get 1T by placing the Tail in any of the 4 flips _ _ _ _ => 4 ways

Cases in which we will get 4H

Case in which we get 4 heads = 1 (HHHH)

=> P(At least 3 heads) = (Cases in which we will get 3 or 4 Heads) / 16 =  \frac{4 + 1 }{ 16}  =  \frac{5}{16}

So,  Answer will be C 
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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If a fair coin is tossed 4 times, what's the probability that at least

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