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# P of heads if 0.6 in a coin toss. Coin is tossed 5 times.

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Manager
Joined: 27 Sep 2006
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P of heads if 0.6 in a coin toss. Coin is tossed 5 times. [#permalink]  02 Feb 2007, 18:04
P of heads if 0.6 in a coin toss. Coin is tossed 5 times. What the P that heads come up atleast 4 times?

5(0.6)^4 (0.4) + 0.6^5
Senior Manager
Joined: 24 Oct 2006
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p of head = 0.6 and p of tail = 0.4
1) p of h at 4/5= 0.6*0.6*0.6*0.6*0.4 = (0.6)^4*0.4
since there are 5 ways to get this => 5*(0.6)^4*0.4
2)since q asks for p of h atleast 4 times which means that we could get h all the 5 times which is 0.6^5
so the ans is 1+2
Manager
Joined: 10 Dec 2005
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The questions is asked what is the prob. of getting head at least 4 times:

So there are two cases here:

1.) We get head on all the first 4 tries and on the last try we get a tail:

Let's solve this:

Therefore, prob. of tail = 0.4

prob. of getting head in first 4 tries is: 0.6 * 0.6 * 0.6 * 0.6 = 0.6^4
0n the last try let's say we get a tail, prob. of that is: 0.4

Hence the prob. of the case 1 is: (0.6^4) * 0.4

This can be done in 5 different ways hence prob is: 5((0.6^4) * 0.4)

2.) We get head on all the 5 tries:

Let's solve this
prob. of getting head on all the 5 tries is: 0.6 * 0.6 * 0.6 * 0.6 * 0.6 = 0.6^5

Therefore, total prob = 5((0.6^4) * 0.4) + 0.6^5
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