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# What is the probability of tossing a coin five times and having heads

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What is the probability of tossing a coin five times and having heads  [#permalink]

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04 Nov 2019, 00:53
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Difficulty:

65% (hard)

Question Stats:

54% (01:52) correct 46% (01:46) wrong based on 70 sessions

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Competition Mode Question

What is the probability of tossing a coin five times and having heads appear at least two times?

(A) 1/32
(B) 1/16
(C) 15/16
(D) 13/16
(E) 7/8

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Re: What is the probability of tossing a coin five times and having heads  [#permalink]

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04 Nov 2019, 01:09
1
Probability of having at least 2 heads = 1 - (probability of 1 heads + prob of no heads)

1 - {5C1(1/2)^1 (1/2)^4 + (1/2)^5}

1- {5/32 + 1/32} = 26/32

= 13/16

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Re: What is the probability of tossing a coin five times and having heads  [#permalink]

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04 Nov 2019, 01:20
2
1
Formula: Probability of getting r heads when coin is tossed n times = nCr*$$p^r*q^{n-r}$$
Where p = probability of getting heads
& q = probability of getting tails

Probability (0 heads) = $$5C_0*(1/2)^5 = 1/32$$
Probability (1 head) = $$5C_1*(1/2)^5 = 5/32$$

Probability(0 heads or 1 head) = $$1/32 + 5/32 = 6/32 = 3/16$$

—> Required Probability = $$1 - 3/16 = 13/16$$

IMO Option D

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Re: What is the probability of tossing a coin five times and having heads  [#permalink]

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04 Nov 2019, 01:29
1
P of no head = 1/32
P of 1 head = 5c1* 1/16*1/2 ; 5/32
P of atmost 1 head = 1/32+ 5/32 ; 6/32 ; 3/16
atleast 2 times ; 1-3/16 ; 13/16
IMO D

What is the probability of tossing a coin five times and having heads appear at least two times?

(A) 1/32
(B) 1/16
(C) 15/16
(D) 13/16
(E) 7/8
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What is the probability of tossing a coin five times and having heads  [#permalink]

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Updated on: 05 Nov 2019, 04:46
Quote:
What is the probability of tossing a coin five times and having heads appear at least two times?

(A) 1/32
(B) 1/16
(C) 15/16
(D) 13/16
(E) 7/8

TTTTH: (1/2)^4 * (1/2) * 5!/4! = 1/16 * 1/2 * 5 = 5/32
TTTTT: (1/2)^5 * 5!/5! = 1/32
1 - P(NOT) = 1 - (6/32) = 13/16

Originally posted by exc4libur on 04 Nov 2019, 04:39.
Last edited by exc4libur on 05 Nov 2019, 04:46, edited 1 time in total.
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Re: What is the probability of tossing a coin five times and having heads  [#permalink]

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04 Nov 2019, 04:58
1
For a head to appear at least two times, we have 5C2 + 5C3 + 5C4 + 5C5 = 10+10+5+1=26 total possibilities
Total events = 2^5 = 32
P(at least 2H) = 26/32 = 13/16.

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Re: What is the probability of tossing a coin five times and having heads  [#permalink]

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04 Nov 2019, 05:28
1
Total possible cases are 2^5=32

Since its At least 2, below are the possible cases

Only2+only3+only4+all5

In only 2 case, there are 3 cases of tails
In only3, other 2 are tails
In only 4, other 1 is tail
In all5, no case of tails

So except above 6cases, other 26cases satisfies above condition.

SO probability is 26/32

OA:D ,13/16
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Re: What is the probability of tossing a coin five times and having heads  [#permalink]

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04 Nov 2019, 10:28
2
A coin is tossed 5 times,
possibility each time: 2 (1 head, 1 tail)
=> total outcomes = 2^5 = 32.

minimum 2 heads means: (1) HHTTT, (2) HHHTT, (3) HHHHT and (4) HHHHH

1. total possibilities of HHTTT: 5! / (2! x 3!) = 10 nos
2. total possibilities of HHHTT: 5! / (3! x 2!) = 10 nos
3. total possibilities of HHHHT: 5! / (4! x 1!) = 5 nos
4. total possibilities of HHHHH: 5! / (5! x 0!) = 1 nos

=> total possibilities of minimum 2 heads = 10+10+5+1 = 26 nos

=> P ( min. 2 heads) = favourable outcomes / total outcomes
= 26/32
= 13/16

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Re: What is the probability of tossing a coin five times and having heads  [#permalink]

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04 Nov 2019, 13:03
First we count What is the probability that the coin lands on the head for one time and a never apeares on head.
(1/2)⁴ × 1/2=1/32
(1/2)^5=1/32
1- 2/32 =30/32=15/16

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Re: What is the probability of tossing a coin five times and having heads  [#permalink]

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04 Nov 2019, 14:04
1
Asked: What is the probability of tossing a coin five times and having heads appear at least two times?

Total cases = 2^5 = 32
Unfavorable cases = Head not appearing + Head appearing once = 1 + 5 = 6
Favorable cases = 32 - 6 = 26

Probability = Favorable cases / Total cases = 26/32 = 13/16

IMO D
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Re: What is the probability of tossing a coin five times and having heads  [#permalink]

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04 Nov 2019, 14:44
1
What is the probability of tossing a coin five times and having heads appear at least two times?

Probability of getting heads 1 time= 5C1 $$(\frac{1}{2})^5$$
Probability of getting all tails= $$(\frac{1}{2})^5$$

Probability of getting heads at least 2 times=$$1-\frac{5}{32}-\frac{1}{32}$$= $$\frac{26}{32}$$=$$\frac{13}{16}$$
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Re: What is the probability of tossing a coin five times and having heads  [#permalink]

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04 Nov 2019, 15:40
1
We need to determine the probability of seeing heads 2, 3, 4, or 5 times when a coin is flipped 5 times.

It is easier to calculate the opposite event and subtract it from 1.

Opposite event = probability of seeing 0 head or probability of seeing 1 head

Total number of outcomes = 2x2x2x2x2 = 32

Favourable outcomes :
0 Head i.e TTTTT =1 event
1 Head i.e HTTTT = 5 events since H can be arranged anywhere

Probability of seeing 0 head or probability of seeing 1 head $$= \frac{1}{32} + \frac{5}{32}$$

$$P = 1 - \frac{6}{32} =\frac{13}{16}$$
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Re: What is the probability of tossing a coin five times and having heads  [#permalink]

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06 Nov 2019, 01:23
Bunuel wrote:

Competition Mode Question

What is the probability of tossing a coin five times and having heads appear at least two times?

(A) 1/32
(B) 1/16
(C) 15/16
(D) 13/16
(E) 7/8

Are You Up For the Challenge: 700 Level Questions

$$(!5/!2*!3)+(!5/!3*!2)+(!5/!4*!1)+(!5/!5)/2^5$$
=26/32
=13/16
D:)
Re: What is the probability of tossing a coin five times and having heads   [#permalink] 06 Nov 2019, 01:23
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