. A box contains 10 balls, numbered 1 through 10 (so the balls are distinct). a. A ball is drawn from the box at random. Compute the probability that the number on the ball was 3, 4, or 5. b. A ball is chosen at random and then a second ball is chosen at random from the remaining nine balls. Find the probability that the numbers on the two selected balls differ by 2 or more. c. Three balls are chosen (with replacement). Find the probability that the sum of the numbers on the balls is even.

A) 0.30

B) 0.9

C) 0.4

Step-by-step explanation:

Number of balls = 10

A ) probability that a ball drawn at random is numbered 3,4 or 5

 number on ball to be drawn = 3   i.e 3,4 or 5

 total number of balls = 10

hence the probability = 3 / 10 = 0.30

B ) probability that number written on two different balls drawn at random differs by 2 or more

p( numbers differ by 1 ) = 9 * (1/10) * (1/9) =  0.1

p( numbers on two balls differ by 2 or more ) = 1 - p( numbers differ by 1 )

                                                                           = 1 - 0.1 =  0.9

C ) Probabilty that the sum of the numbers on 3 balls chosen is even

even numbers = 5 which are ( 2,4,6,8,10 )

The even numbers that can be gotten by summation of three balls are

(4.6,8,10 ) = 4

hence the probability of picking three balls with replacement  whose sum = even number will be

= 4 / 10 = 0.4  

-3

step-by-step explanation:

a drawing really does here:

so i draw the horizontal line y=2 and the vertical line x=-2 at this intersection i put b (this is where my right angle is going to be).   so point b is at (-2,2).   point a is 5 units long and is also on y=2 so this point has to be (3,2) or (-7,2) -doesn't matter i will go with (3,2).

now we know c is at (-2,y) we don't know the y yet bet we know that c is on x=-2.

we have the area of the triangle is .5bh=12.5

we know the base length is 5 (ab)

we have the height is (2-y) if you look at your

plug in

.5(5)(2-y)=12.5

solve for y to get the y-coordinate for c

2.5(2-y)=12.5

divide both sides by 2.5 giving:

2-y=5

now subtract 2 on both sides

-y=3

y=-3

15: 24

62.5%

step-by-step explanation: