Answer:
0.09923
Step-by-step explanation:
We will first use combination which gives total number of ways of selecting r objects out of n
[tex]\limits^nC_{r} =\frac{n!}{r! (n-r)!}[/tex]
for :
20C14 =38760 (using calculator)
so assuming sequence of 20 terms, there are 38760 ways of picking the 20 terms.
Each toss there are 2 possible outcomes, total possible outcomes for 20 tosses combined are:
Total possible outcome = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x2 x 2 x 2 x 2 x 2 = [tex]2^{20}[/tex] =1048576
As given, the girl predicts 14 tosses correctly. so, the probability of getting 14 tosses correct is : P(14 Right)= [tex]\frac{20C14}{2^{20} }[/tex] =[tex]\frac{38760}{1048576}[/tex] = 0.03696
and So on :
P (15 Right) =[tex]\frac{20C15}{2^{20} }[/tex] =[tex]\frac{15504}{1048576}[/tex]=0.01478
P (16 Right) =[tex]\frac{20C16}{2^{20} }[/tex] =[tex]\frac{4845}{1048576}[/tex]=0.0462
P (17 Right) =[tex]\frac{20C17}{2^{20} }[/tex] =[tex]\frac{1140}{1048576}[/tex]=0.001087
P (18 Right) =[tex]\frac{20C18}{2^{20} }[/tex] =[tex]\frac{190}{1048576}[/tex]=0.000181
P (19 Right) =[tex]\frac{20C19}{2^{20} }[/tex] =[tex]\frac{20}{1048576}[/tex]=0.000019
P (20 Right) =[tex]\frac{20C20}{2^{20}}[/tex] =[tex]\frac{1}{1048576}[/tex]=0.000000953
We add all probabilities to get:
Probability of getting 14 or more correct is : P (14 or more) = P(14 Right) + P (15 Right) + ..... + P(20 right) = 0.03696 + 0.01478+0.0462+0.001087+0.000181+0.000019+0.000000953 = 0.09923
