This is to do with independant events & probability trees There is a bag filled with 3 blue and 5 red marbles.
A marble is taken at random from the bag, the colour is noted and then it is replaced.
Another marble is taken at random.
What is the probability of getting 2 reds?

The probability of getting two red marbles is P = 0.141

Step-by-step explanation:

We know that in the bag there are 3 blue marbles and 5 red marbles, then there is a total of 8 marbles in the bag.

The probability of taking at random a red marble is equal to the quotient between the number of red marbles and the total number of marbles, this is:

p = 3/8

Suppose we got a red marble:

Now we replace the red marble we took, so in the bag there are again 3 red marbles and 8 total marbles, then the probability of getting another red marble is again:

q = 3/8

The joint probability (this is, the probability of both events happening) is equal to the product of the individual probabilities, with gives us:

P = p*q = (3/8)*(3/8) = 9/64 = 0.141

step-by-step explanation:

equation

you are asked to write the equation

  expression = 0

using the given expression. when you do that, you have

  2x^2-2x-12 = 0

factoring

you can see that each of the coefficients is even, so a factor of 2 can be removed immediately.

  2(x^2 -x -6) = 0

if you multiply the binomials (x+a)(x+b), you get

  (x +a)(x +b) = x^2 +(a+b)x +ab

this tells you the coefficient of x is the sum of two factors of the constant term. here, that means -1 is the sum of two factors of -6. we want to know those factors so we can factor the trinomial.

  -6 = -1×6 = -2×3 = -3×2 = -6×1

the factor pair that sums to -1 is {-3, 2}, so our factorization is

  2(x -3)(x +2) = 0

solutions

the solutions to this equation are the values of x that make the product zero. a product is zero only when only of the factors of the product is zero. here, that means

  x - 3 = 0

  x = 3 . . . add 3 to both sides of the equation

or

  x +2 = 0

  x = -2 . . . add -2 to both sides of the equation

the solutions to the equation are x=3 or x=-2. both of these values of x satisfy the equation—they make it be true.

answer: -1

step-by-step explanation: