A right triangle's longest side is the hypotenuse
let x=longest, y=middle, and z=shortest
x=y+2
y=2z-1
therefore x=(2z-1)+2=2z+1
find z
z^2+y^2=x^2 by Pythagorean theorem
plug in x and y in terms of z
z^2+(2z-1)^2=(2z+1)^2
z^2+4z^2-4z+1=4z^2+4z+1
subtract the right-hand side's value from the left-hand side's
z^2-8z=0
z(z-8)=0
z=0, 8
z cannot be zero as the sides must have some value to it.
Therefore the shortest side is equal to 8
First, let's count:
there are 26 possible outcomes for E1 (black card)
there are 4x9 = 36 possible outcomes for E2, to pick a numbered card (any color)
there are 2x9 =18 possible outcomes for E1 (black) AND E2 (numbered, spade + clower)
the probability of E1 AND E2 is the ratio of the count of possible outcomes for E1 + E2 and the count of all possible outcomes (52 choices to pick a card from the deck):
P(E1 and E2) = 18/52 (34.6%)
And as asked:
P(E1) = 26/52 = 1/2 (50%)
P(E2) = 36/52 = 9/13 (69.2%)
Step-by-step explanation:
I believe this would be A or D
