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A coin that is tossed will land heads or tails, and each outcome has

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Math Expert
Joined: 02 Sep 2009
Posts: 58333
A coin that is tossed will land heads or tails, and each outcome has  [#permalink]

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29 Oct 2018, 01:06
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Difficulty:

15% (low)

Question Stats:

73% (00:41) correct 27% (00:34) wrong based on 74 sessions

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A coin that is tossed will land heads or tails, and each outcome has equal probability. What is the probability that the coin will land heads at least once on two tosses?

A. 1/4
B. 1/3
C. 1/2
D. 2/3
E. 3/4

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Re: A coin that is tossed will land heads or tails, and each outcome has  [#permalink]

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29 Oct 2018, 05:15
The probability of at least one heads in two flips = 1 - probability of no heads

Probability of no heads in both flips = 1/2 * 1/2 (both are tail)

so 1 - 1/4 = 3/4

Or we can do it in the longer way

One heads, one tails = 1/2 * 1/2 = 1/4
One tail and one heads = 1/2 * 1/2 = 1/4
Two heads = 1/2 * 1/2 = 1/4

Add them we get 3/4

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A coin that is tossed will land heads or tails, and each outcome has  [#permalink]

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29 Oct 2018, 05:49
Bunuel wrote:
A coin that is tossed will land heads or tails, and each outcome has equal probability. What is the probability that the coin will land heads at least once on two tosses?

A. 1/4
B. 1/3
C. 1/2
D. 2/3
E. 3/4

Total outcomes when a coin is tossed twice = 2*2 = 4

METHOD 1:
Case 1: Exactly 1 Head outcomes will be HT or TH i.e. 2 outcomes
Case 2: Exactly 2 Head outcomes will be HH i.e. 1 outcome

Favourable Outcomes = 3

Probability = 3/4

METHOD 2:

Unfavourable case is when None of the toss results in a Head i.e. Both Tails i.e. TT i.e. 1 outcome

Unfavourable Probability = 1/4

Favourable Probability = 1- Unfavourable probability = 1- (1/4) = 3/4

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Re: A coin that is tossed will land heads or tails, and each outcome has  [#permalink]

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30 Oct 2018, 03:24

Solution

Given:
• Each outcome of a fair coin has equal probability

To find:
• Probability of atleast one heads

Approach and Working:
• Total number of outcomes = 2 * 2 = 4, which are {HH, HT, TH, TT}
o Among these 3 outcomes have atleast one heads, {HH, TH, HT}

• Therefore, the probability of atleast one heads = $$\frac{3}{4}$$

Hence, the correct answer is Option E

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Re: A coin that is tossed will land heads or tails, and each outcome has   [#permalink] 30 Oct 2018, 03:24
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