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sdas [7]
3 years ago
11

An envelope contains three cards: a black card that is black on both sides, a white card that is white on both sides, and a mixe

d card that is black on one side and white on the other. You select one card at random and note that the side facing up is black. What is the probability that the other side is also black?
Mathematics
1 answer:
Over [174]3 years ago
5 0

Answer:

There is a  2/3  probability that the other side is also black.

Step-by-step explanation:

Here let B1: Event of picking a card that has a black side

B2: Event of picking a card that has BOTH black side.

Now, by the CONDITIONAL PROBABILITY:

P(B_2/B_1 )  = \frac{P(B_1\cap B_2)}{P(B_1)}

Now, as EXACTLY ONE CARD has both sides BLACK in three cards.

⇒ P (B1 ∩ B2) = 1 /3

Also, Out if total 6 sides of cards, 3 are BLACK from one side.

⇒ P (B1 ) = 3 /6 = 1/2

Putting these values in the formula, we get:

P(B_2/B_1 )  = \frac{P(B_1\cap B_2)}{P(B_1)} = \frac{1}{3}  \times\frac{2}{1} = \frac{2}{3}

⇒ P (B2 / B1)  =  2/3

Hence, there is a  2/3  probability that the other side is also black.

 

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den301095 [7]

Answer:

Step-by-step explanation:

The best way to do this is to first remove the parenthesis by distributing the negative into them. Then we will group the like terms together, moving their respective signs with them, then we will simplify.  For the first one, after distributing the negative into the parenthesis (remember that a negative in front of a set of parenthesis containing a polynomial changes the signs in front of each term within the polynomial; negatives become positives and positives become negatives):

3x^2-6x+11-10x^2+4x-6 and then grouping like terms next to each other:

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The above then simplifies to

-7x^2-2x+5

The next one, after distributing the negative into the parenthesis:

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7x^2+2x-5

Now for the last one:

12x^2+6x-5-5x^2-8x+12 and

12x^2-5x^2+6x-8x-5+12 which simplifies to

7x^2-2x+7

6 0
3 years ago
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lana [24]

Answer:

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Step-by-step explanation:

Hope this helps :))

6 0
3 years ago
For f(x) = 3x+1 and g(x) = x^2-6, find (g/f)(x)
nexus9112 [7]
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3 years ago
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Step-by-step explanation:

   

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