Question

Draw an uncertain event that is characterized by the binomial distribution associated with a sample size of N = 4. Hint: Express in terms of the number of “successes” found in a sample.

Answer 1

Let our event be the toss of coin :

Outcomes on each toss : Heads(H) / Tails(T)

Probabality (Heads ) = P( Tails) = 0.5

and let us call P=(Probabality of Success ) = getting a Heads = P(H) = 0.5

Probabality of failure ) = 1- P = 0.5

N =4

So by binomial distribution formula for probabality of success of 4 such coin throws for r time sucesses given by

P(success) =  ^N C _r P ^r ( 1 - P ) ^{N -r}

= ⁴ C _r 0.5 ⁴

^{r = 0,1,2,3.or 4}

^{r = 0 means 0 heads in the 4 coin toss}