Head-Tail Question

[goelmohit2002]

Hi All,

Probability of getting a head on a toss of non fair coin is 0.6. In 6 tosses of a coin, what is the probability of getting atleast 5 heads ?

OA = Will post after some discussion.

Thanks
Mohit

[sharok50]

nCr X p^r X q^n-r

=> 6C5 X (.6)^5 X (.4)^6-5

i hope this is the way.

[goelmohit2002]

nCr X p^r X q^n-r

=> 6C5 X (.6)^5 X (.4)^6-5

i hope this is the way.

Yes thanks. The above is the OA.

[Ben Ku]

sharok50's response only takes into account the probability of tossing exactly 5 heads in 6 tosses. However, it does not add in the probability of tossing 6 heads.

I look at the problem this way:
P(5 Heads) + P(6 Heads)

P(6 Heads) is easy. Each toss has a 0.6 chance of being heads, so P(6 Heads) = (0.6)^6.

P(5 Heads) is a bit more complicated, because there are different ways to get 5 heads. One combination of getting 5 Heads is HHHHHT. The probability of this combination is (0.6)(0.6)(0.6)(0.6)(0.6)(0.4) = (0.6)^5(0.4). [The 0.4 is there because that's the probability of getting tails.] Using the anagram method, there are 6!/5! = 6 different combinations of getting 5 Heads. So P(5 Heads) = (6)(0.6^5)(0.4) = (4)(0.6^6)

P(5 Heads) + P(6 Heads) = (4)(0.6^6) + (0.6^6) = 5(0.6^6)