You watch a match between two tennis players: bill and tom. you know that one of them is ranked first in the district and the other is ranked 3rd but you don’t know which is which. you also know that the probability that the 3rd ranked player wins any game is p < 1/2, independently of the outcome of other games. you watch ten games. bill wins eight and tom wins two. what is the probability that bill is the first ranked player? show your work.

To solve this problem we need the concepts about Bernoulli variables.

Then we define the two probabilities and states that we have

We have two individuals, Bill and Tom.

Let's consider:

for the 8/10 probability that Bill is first ranker.

For the probability that Tom is the first ranker (Or bill is third ranker)

Then,

Of 10 games played, Bill has won 8.

P(X=1) = 0.8

if he is naked in public on purpose then yes. that is a crime and you should call the police as he could be a threat to females/ might flash.

something that characterises a right triangle is the fact that we may use pythagoras' theorem to find any one of its sides given that we have the length of the other two sides. here, we have the length of the hypotenuse, √(87) yd, and one other side, √(23) yd, thus we can easily find the length of the remaining side using pythagoras' theorem as defined below:

c^2 = a^2 + b^2, where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

thus, given that c = √(87) and a = √(23), we may substitute these into the formula we defined above to get:

c^2 = a^2 + b^2

(√87)^2 = (√23)^2 + b^2 (substitute c = √87 and a = √23 into the equation)

87 = 23 + b^2 (evaluate (√87)^2 = 87 and (√23)^2 = 23 - remember that the square root of a number, squared will equal that very same number)

64 = b^2 (subtract 23 from both sides)

√64 = b (take the square root of both sides)

8 = b (evaluate √64 = 8)

therefor, the length of the unknown leg in the right triangle is 8 yd (first answer).