A standard card deck has 52 cards consisting of 26 black and 26 red cards. Three cards are dealt from a shuffled deck, without replacement. Complete parts a through c below. a. Determine whether the following statement is true or false. The probability of being dealt three black cards is one half times one half times one half equals one eighth . If true, explain why. If false, show how to get the correct probability.

6 / 51

Step-by-step explanation:

It is false.

Reason:

The probability of picking a black card at first is:

26 / 52 = 1/2

There are now 25 black cards and 51 cards in total.

The probability of picking another black card, if there's no replacement is now:

25 / 51

Now, there are 24 black cards and 50 cards left in total.

The probability of picking a black card without replacement now becomes:

24 / 50 = 12 / 25

Hence, the probability of picking three black cards without replacement is:

1/2 * 25/51 * 12 / 25 = 300 / 2550

In simplest form, it is 6 / 51

1A. A graph shows the solution of the equation to be x=2.

1B. The extraneous solution is x=-3. That solution requires the square root function return a negative value. It does not satisfy the original equation.

If you solve this equation by squaring both sides then solving the resulting quadratic, you are finding solutions to
   x² +x -6 = 0
which factors to
   (x+3)(x-2) = 0
and has solutions x=-3, x=2.

1C. An "extraneous" solution is one that does not satisfy the original equation, but may arise as a consequence of some solution methods.

2A. We can choose the extraneous root to be x=-5 so the equation being solved is (x-7)(x+5) = 0 = x² -2x -35. If we choose A=1, then the squared equation is (x+1)² -4x -36 = 0, and we have B=4, C=36. Our equation is
 

2B. Squaring both sides gives
   x² +2x +1 = 4x +36
   x² -2x -35 = 0 . . . . . . . . subtract the right side
   (x -7)(x +5) = 0 . . . . . . .factor
Solutions are x=7, x=-5.
x=-5 is extraneous.

2C. Another equation with the same set of solutions (real and extraneous) is