Consider an urn containing a large number of coins, and suppose that each of the coins has some probability p of turning up heads when it is flipped. however, p varies from coin to coin. suppose that the composition of the urn’s contents is such that if a coin is selected at random from it, then the value of p for the coin can be regarded as being the value of a random variable that is uniformly distributed over [0, 1]. if a coin is selected at random from the urn and flipped twice, what is the probability that the first flip results in a head?

The required probability is

Step-by-step explanation:

Consider the provided information.

We need to find the probability that the first flip results in a head.

Therefore probability of lending head is

The first flip is head can be calculated as:

Integrate the above function as shown below:

Hence, the required probability is

check above link.

graphically?   well, you graph them both, the solutions is where they both intersect each other, since there are two solutions, meaning they will meet twice, or namely the linear will run into the quadratic curve twice, and where they meet, those x,y coordinates are the solutions to the system.

the formula for the equation of a circle is (x – h)2+ (y – k)2 = r2, where (h, k) represents the coordinates of the center of the circle, and r represents the radius of the circle. if a circle is tangent to the x-axis at (3,0), this means it touches the x-axis at that point.