Answer:
No, the probability doesn't seem to verify the claim as it is greater than 0.5.
Step-by-step explanation:
Given information:
Let X be the number of times the person predicts correctly about the outcome of a coin and follows a binomial distribution.
The probability (p) that the person predicts correctly about the outcome of a coin is 16/20.
Now, the probability of being correct 16 or more times by guessing is calculated below:
[tex]P(X\geq 16)= P(X=16)+ P(X=17)+ P(X=18)+ P(X=19)+P(X=20)[/tex]
= [tex]{^20}C_16[/tex] [tex]\left(\frac{16}{20}\right)^{16}}\times \left(1-\frac{16}{20}\right)^{20-16}[/tex] +
[tex]{^20}C_17[/tex] [tex]\left(\frac{16}{20}\right)^{17}}\times \left(1-\frac{16}{20}\right)^{20-17}[/tex]+.......+
[tex]{^20}C_20[/tex][tex]\left(\frac{16}{20}\right)^{20}\times\left(1-\frac{16}{20}\right)[/tex]
= 0.6296
Hence, the probability doesn't seem to verify the claim as it is greater than 0.5.
