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Manager
Joined: 12 Nov 2016
Posts: 124

Kudos [?]: 12 [0], given: 71

Location: Kazakhstan
Concentration: Entrepreneurship, Finance
GMAT 1: 620 Q36 V39
GMAT 2: 650 Q47 V33
GPA: 3.2

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16 Dec 2017, 11:10
Bunuel wrote:
Braving the Binomial Probability

BY Karishma, VERITAS PREP

Question 2: For one toss of a certain coin, the probability that the outcome is heads is 0.7. If the coin is tossed 6 times, what is the probability that the outcome will be tails at least 5 times?

Solution: This question is very similar to the questions we saw in the Probability book. The only difference is that we are not tossing a fair coin. The probability of getting heads is 0.7 not 0.5. So the probability of getting tails must be 0.3 since the total probability has to add up to 1.

The only acceptable cases are those in which we get ‘tails’ on all 6 tosses or we get tails on exactly 5 of the 6 tosses.

P(Tails on all 6 tosses) = $$(0.3)*(0.3)*(0.3)*(0.3)*(0.3)*(0.3) = (0.3)^6$$

[color=#ffff00]P(Tails on exactly 5 tosses and Heads on one toss) = $$(0.3)^5*(0.7)*6$$

We multiply by 6 because 5 tails and 1 heads can be obtained in 6 different ways: HTTTTT, THTTTT, TTHTTT, TTTHTT, TTTTHT, TTTTTH

Probability that the outcome will be tails at least 5 times = Probability that the outcome will be tails 5 times + Probability that the outcome will be tails 6 times

Probability that the outcome will be tails at least 5 times = $$(0.3)^6 + (0.3)^5*(0.7)*6$$
[/color]

I am confused by this multiplication by 6 - why when probability that the outcome will be tails 6 times we simply (0.3)^6 and when probability that the outcome will be tails 5 times - we do multiply (0.3)^5*(0.7) by 6? Why tails on all 6 tosses is (0.3)^6 without any multiplication by 6! and Tails on exactly 5 tosses and heads on one toss needs to be multliplied by 6?

Last edited by Erjan_S on 16 Dec 2017, 21:32, edited 1 time in total.

Kudos [?]: 12 [0], given: 71

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16 Dec 2017, 11:22
Erjan_S wrote:
Bunuel wrote:
Braving the Binomial Probability

BY Karishma, VERITAS PREP

Question 2: For one toss of a certain coin, the probability that the outcome is heads is 0.7. If the coin is tossed 6 times, what is the probability that the outcome will be tails at least 5 times?

Solution: This question is very similar to the questions we saw in the Probability book. The only difference is that we are not tossing a fair coin. The probability of getting heads is 0.7 not 0.5. So the probability of getting tails must be 0.3 since the total probability has to add up to 1.

The only acceptable cases are those in which we get ‘tails’ on all 6 tosses or we get tails on exactly 5 of the 6 tosses.

P(Tails on all 6 tosses) = $$(0.3)*(0.3)*(0.3)*(0.3)*(0.3)*(0.3) = (0.3)^6$$

P(Tails on exactly 5 tosses and Heads on one toss) = $$(0.3)^5*(0.7)*6$$

We multiply by 6 because 5 tails and 1 heads can be obtained in 6 different ways: HTTTTT, THTTTT, TTHTTT, TTTHTT, TTTTHT, TTTTTH

Probability that the outcome will be tails at least 5 times = Probability that the outcome will be tails 5 times + Probability that the outcome will be tails 6 times

Probability that the outcome will be tails at least 5 times = $$(0.3)^6 + (0.3)^5*(0.7)*6$$

I am confused by this multiplication by 6 - why when probability that the outcome will be tails 6 times we simply (0.3)^6 and when probability that the outcome will be tails 5 times - we do multiply (0.3)^5*(0.7) by 6? Why tails on all 6 tosses is (0.3)^6 without any multiplication by 6! and Tails on exactly 5 tosses and heads on one toss needs to be multliplied by 6?

Hi Erjan_S

when you are sure that only tails will occur, then the situation will look like TTTTTT i.e only 1 possibility. Hence probability of tails on all 6 counts will be (0.3)^6

but when 5 tails and 1 heads has to occur, then this situation throws up additional possibilities -

HTTTTT, the probability of this possibility is 0.7*(0.3)^5

THTTTT, the probability of this possibility is 0.7*(0.3)^5

TTHTTT, the probability of this possibility is 0.7*(0.3)^5

TTTHTT, the probability of this possibility is 0.7*(0.3)^5

TTTTHT, the probability of this possibility is 0.7*(0.3)^5

TTTTTH, the probability of this possibility is 0.7*(0.3)^5

Hence total possibility in this case will be sum of all the above possibilities, which simply means you multiply 0.7*(0.3)^5 by 6

Kudos [?]: 376 [0], given: 42

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