Question

a weighted coin has a 0.45 probability of landing on heads. if you toss the coin 6 times, what is the probability of getting heads exactly 4 times? ( round to three decimal places)

Answer 1

`0.186`

Explanation:

`\mathrm{Solution,}\\\mathrm{Suppose\ getting\ head\ is\ a\ success\ and\ getting\ tail\ is\ a\ failure.}\\\mathrm{Now,}\\\mathrm{Probability\ of\ success(p)=0.45}\\\mathrm{Probability\ of\ failure(q)=1-p=1-0.45=0.55}\\\mathrm{Number\ of\ times\ experiment\ is\ done(n)=6}\\\mathrm{Number\ of\ success\ desired(r)=4}\\\mathrm{We\ use\ the\ formula,}\\\mathrm{P(r)=nCr* p^r* q^(n-r)}\\\mathrm{P(4)=6C4* 0.45^4* 0.55^(6-4)}=0.186}`

`\mathrm{So,\ the\ required\ probability\ is\ 0.186.}`