You play a game where you first choose a positive integernand thenflip a fair coinntimes. You win a prize if you get exactly 2 heads. How should youchoosento maximize your chance of winning

Solution :

The probability of winning when you choose n is =  

Apply log on both the sides,

Differentiation, f(x) is

Let us find x for which f' is positive and x for which f' is negative.

      , since

For x ≤ 3, f' > 0 for

That means f(x) is increasing function for n ≤ 3

for x > 4

f' < 0 for n ≥ 4, that means f(n) is decreasing function for n ≥ 4.

Probability of winning when you chose n = 3 is

Probability of winning when you chose n = 4 is

Therefore, we should chose either 3 or 4 to maximize chances of winning.

The probability of winning with an optimal choice is n = 0.375

center= (-2,0)

radius= sqrt2/2

step-by-step explanation:

can i see the following ?

step-by-step explanation: