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

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Math Expert
Joined: 02 Sep 2009
Posts: 59587
If a fair coin is tossed 4 times, what's the probability that at least  [#permalink]

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26 Nov 2018, 03:06
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Difficulty:

45% (medium)

Question Stats:

61% (01:31) correct 39% (01:34) wrong based on 65 sessions

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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

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Re: If a fair coin is tossed 4 times, what's the probability that at least  [#permalink]

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26 Nov 2018, 03:18
2
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
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Re: If a fair coin is tossed 4 times, what's the probability that at least  [#permalink]

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26 Nov 2018, 03:39
1
Bunuel wrote:
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

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
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Re: If a fair coin is tossed 4 times, what's the probability that at least  [#permalink]

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26 Nov 2018, 17:49
1
Bunuel wrote:
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

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
Re: If a fair coin is tossed 4 times, what's the probability that at least   [#permalink] 26 Nov 2018, 17:49
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