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For one toss of a certain coin, the probability that th

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For one toss of a certain coin, the probability that th

by varun289 » Thu Dec 13, 2012 7:06 am
204. For one toss of a certain coin, the probability that the outcome is heads is 0.6. If this coin is tossed 5 times, which of the following is the probability that the outcome will be heads 'at least' 4 times?
(A) (0.6)^5
(B) 2(0.6)^4
(C) 3[(0.6)^4](0.4)
(D) 4[((0.6)^4)(0.4)] + (0.6)^5
(E) 5[((0.6)^4)(0.4)] + (0.6)^5
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by Anindya Madhudor » Thu Dec 13, 2012 8:19 am
At least 4 heads means either 4 or 5 heads.

i. 4 heads:

4 heads can come up in the following ways:
HHHHT HHHTH HHTHH HTHHH THHHH

Probability of each of this occurring = (0.6)^4 * 0.4
Total probability of 4 heads = 5 *[ (0.6)^4 * 0.4]

ii. 5 heads:

This can occur in just 1 way.
Probability of 5 heads = (0.6)^5

You add these two probabilities to arrive at answer E.
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by Jim@StratusPrep » Thu Dec 13, 2012 11:19 am
The probability of it happening 5 times is .6^5 (from there you can narrow to d and e

The probability of it happening 5 times is 5(.6^4 * .4)
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by puneetkhurana2000 » Thu Dec 13, 2012 11:42 am
Heads 5 times -- (0.6)^5

Heads 4 times -- (0.6)^4*(0.4)*(5!/4!) = (0.6)^4*(0.4)*5 ....HHHHT has (5!/4!) ways with different orders so need to multiply by (5!/4!)

Total is -- 5[((0.6)^4)(0.4)] + (0.6)^5

Answer E
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