Answer: The required probability is 
Step-by-step explanation: Given that an urn contains 6 red marbles and 4 black marbles. Two marbles are randomly drawn one by one from the urn without replacement.
We are to find the probability that both drawn marbles are black.
Let E and F denote the events of two marbles one by one without replacement and let S and S' denote the corresponding sample spaces.
Then, we have
Therefore, the probability that both marbles are red is given by
Thus, the required probability is
<h2>
Answer:</h2>
The expression which is equivalent to the following complex fraction is:
<h2>
Step-by-step explanation:</h2>
We are given a expression in terms of two variables x and y as follows:
Now, on taking least common multiple in the numerator as well as in the denominator we have:
which on further simplifying is:
We define the spaces of the man and the woman's independent arrivals.
In this case,
f(man) = 1 (45-15) = 1/30
f(woman)=1/(60-0)= 1/60
f(man)*f(woman) = 1/1800
Probability = P
P (man-woman)< 5 = 1/1800* integral of (y ) with limits of (x+5) and (x-5) from 45 to 15.
P (man-woman) <5 = 1/6
Step-by-step explanation:
By Pythagoras' Theorem,
where c is always the largest number.
a and b can be interchangeable between the 2nd largest and the 3rd largest numbers.
Given a = 8, b = 15 and c = 17,
Since c^2 = a^2 + b^2 , 8 , 15 and 17 are pythagorean triplets.
Now let's move on to 9, 40 and 41.
Since c^2 = a^2 + b^2 , 9 , 40 and 41 are pythagorean triplets.
Last let's move on to 4,7 and 8.
Since a^2+b^2 IS NOT EQUAL to c^2, 4,7 and 8 ARE NOT pythagorean triplets.
