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

step-by-step explanation:

if you meant, "on the way from (3, 2) to (3, 14):

x does not change; y increases by 12.

ensure that you have copied down this problem correctly.   .

this linear equation would have just one solution.

step-by-step explanation:

the reason why this would have one solution is that it is an expression with just one variable. since that variable is not raised to a power, it will always have just one solution.