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Re: A fair coin is tossed 5 times. What is the probability that [#permalink]

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06 Aug 2014, 19:43

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Probability of all tails = 1/32 Probability of 4 tails = 5/32 ------------------------------------------------------------------------------ Probability of all tails or 4 tails = 1/32 + 5/32 = 6/32 = (3/16) ------------------------------------------------------------------------------

Therefore probability of at least 2 heads = 1- Prob of all or 4 tails = 1- (3/16) = 13/16

Re: A fair coin is tossed 5 times. What is the probability that [#permalink]

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07 Aug 2014, 09:22

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Fair coin is tossed 5 times . Hence total number of outcomes = 2^5 = 32.

Problem asks for probability of getting atleast heads twice. Hence if we calculate probability of getting Heads exactly once and probability of not getting Heads at all and subract it from the total probability of the event which is 1 (As total probability of certain event will be always 1) we can get the probability of getting atleast heads twice.

Probability of getting exactly one head and no heads= (Number of possible outcomes [ HTTTT , THTTT, TTHTT, TTTHT, TTTTH , TTTTT] = 6)/ (Total possible outcomes = 32)

=> 6/32 = 3/16

Hence probability of getting atleast heads twice = 1 - (3/16) = 13/16 => Choice [D]

Re: A fair coin is tossed 5 times. What is the probability that [#permalink]

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05 Jan 2017, 06:12

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Here are the numbers to remember:

1 3 3 1 1 4 6 4 1 1 5 10 10 5 1

The first row applies to 3 flip questions, the second to 4 flip questions and the third to 5 flip questions. If we want at least 2 heads, we want 2 heads, 3 heads, 4 heads OR 5 heads. Pretty much whenever we see "OR" in probability, we add the individual probabilities.

Looking at the 5 flip row, we have 1 5 10 10 5 1. For 2H, 3H, 4H and 5H we add up the 3rd, 4th, 5th and 6th entries: 10+10+5+1=26.

Summing the whole row, we get 32.

So, the chance of getting at least 2 heads out of 5 flips is 26/32 = 13/16.
_________________

Re: A fair coin is tossed 5 times. What is the probability that [#permalink]

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05 Jan 2017, 06:12

Here are the numbers to remember:

1 3 3 1 1 4 6 4 1 1 5 10 10 5 1

The first row applies to 3 flip questions, the second to 4 flip questions and the third to 5 flip questions. If we want at least 2 heads, we want 2 heads, 3 heads, 4 heads OR 5 heads. Pretty much whenever we see "OR" in probability, we add the individual probabilities.

Looking at the 5 flip row, we have 1 5 10 10 5 1. For 2H, 3H, 4H and 5H we add up the 3rd, 4th, 5th and 6th entries: 10+10+5+1=26.

Summing the whole row, we get 32.

So, the chance of getting at least 2 heads out of 5 flips is 26/32 = 13/16.
_________________

Re: A fair coin is tossed 5 times. What is the probability that [#permalink]

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05 Jan 2017, 07:24

For all these kind of questions we can answer using this concept ( hope all of you might have studied during your school days):

Probability of 'r' success out of 'n' trials = = nCr (P)^r (Q)^n-r

P - probability of success Q - probability of failure

According to this question : We need to find probability of head >= 2 out of 5 trials. P - probability of success = 1/2(probability of getting head out of a toss) Q - probability of failure= 1/2(probability of getting tail out of a toss)

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