Suppose an unfair coin comes up heads 338 of the time if it

Suppose an unfair coin comes up heads 33.8% of the time if it is flipped. It the coin is flipped 14 times, what is the probability that: it comes up tails exactly 10 times? it comes up heads fewer than 3 times?

Solution

a)p=1-(33.8/100) =0.662

n=14

x=10

P(x=10) =¹⁴C₁₀(0.662)¹⁰(1-0.662)^14-10

P(x=10) =0.2111936

probability that it comes up tails exactly 10 times is 0.2111936

b)

p=(33.8/100) =0.338

n=14

x<=3

P(x<3) =[¹⁴C₀0.338⁰0.662¹⁴]+[¹⁴C₁0.338¹0.662¹³]+[¹⁴C₂0.338²0.662¹²]

P(x<3) =0.0989464

probability that it comes up heads fewer than 3 times is 0.0989464