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Probability of the toss of a coin 5 times

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by vishal.pathak » Sat Nov 19, 2011 12:43 am
For one toss of a certain coin, the probability that the outcome is Heads is 0.6. If the coin is tossed 5 times , which of the following is the probability that the outcome will be heads atleast 4 times ?
A) 5(0.6)^4(0.4) + (0.6)^5.
B) 4(0.6)^4(0.4) + (0.6)^5.
C) 3(0.6)^4(0.4) + (0.6)^5.
D) 4(0.6)^4(0.4) + (0.4)^5.
E) 4(0.6)^4(0.4) + (0.5)^5.
OA A
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by shankar.ashwin » Sat Nov 19, 2011 1:25 am
Atleast 4 heads is 4 heads 1 tail or all 5 heads.

All 5 heads probability will be (0.6)^5

4 heads 1 tail.

4 heads in 5 can be distributed in 5C4 = 5 ways.

Now P(head) = 0.6 and P(tail) = 0.4

So, combing we have 5(0.6)^4*(0.4) (i.e HHHHT and its possible arrangements)


So adding the 2 cases we have 5(0.6)^4(0.4) + (0.6)^5. A IMO
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by vishal.pathak » Sat Nov 19, 2011 1:32 am
shankar.ashwin wrote:Atleast 4 heads is 4 heads 1 tail or all 5 heads.

All 5 heads probability will be (0.6)^5

4 heads 1 tail.

4 heads in 5 can be distributed in 5C4 = 5 ways.

Now P(head) = 0.6 and P(tail) = 0.4

So, combing we have 5(0.6)^4*(0.4) (i.e HHHHT and its possible arrangements)


So adding the 2 cases we have 5(0.6)^4(0.4) + (0.6)^5. A IMO
Yeah very true. I didnt read the options correctly. From the looks it appeared that 4 is multiplied to 0.4 instead of being a power of 0.6.

Thanks anyways
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