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Natasha_Volkova [10]
2 years ago
9

1. You have three standard decks of cards in front of you. What is the probability of drawing a heart card from all three decks?

Mathematics
1 answer:
Paladinen [302]2 years ago
7 0

Answer:

1.56%

Step-by-step explanation:

A standard deck of cards has 52 cards, and 13 of these are hearts, as there are 4 suits, and 52/4=13. This means the probability of choosing a heart card from a deck of cards is 1/4, or 25%. Now to find the probability of doing this from 3 decks in a row, we simply cube 1/4 to get 1/64, and in percentage this is ~1.56%.

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Calculate the expected value, the variance, and the standard deviation of the given random variable X. (Round all answers to two
Tom [10]

Answer:

E (X) = 1.8

Var (X) = 0.36

σ = 0.6

Step-by-step explanation:

Solution:-

- Denote the random variable X : is the number of red marbles that Suzan has in her hand after she selects three marbles.

- Total sample space (bag) have the following quantity of colored marbles:

                Bag : { 3 Red , 2 Green }

- Suzan selects three marbles from the bag. The Event (X) defines the number of red marbles out of 3.

- The total number of outcomes / selections for randomly selecting 3 balls from the bag:

               All outcomes = 5 C 3 = 10

- The probability distribution of the random variable X, we will use combinations to determine the required probabilities:

  X = 1 red marble:

        P ( X = 1 ) : Suzan chooses 1 Red marble from the available 3 red marble and 2 green marbles.

        P ( X = 1 ) = [ 3C1*2C2 ] / all outcomes = (3*1) / 10 = 0.3

X = 2 red marble:

        P ( X = 2 ) : Suzan chooses 2 Red marble from the available 3 red marble and 1 green marbles.

        P ( X = 2 ) = [ 3C2*2C1 ] / all outcomes = (3*2) / 10 = 0.6

X = 3 red marble:

        P ( X = 3 ) : Suzan chooses 3 Red marble from the available 3 red marble.

        P ( X = 3 ) = [ 3C3] / all outcomes = (1) / 10 = 0.1

- The probability distribution is as follows:

          X :         1                 2                3

       P (X):       0.3            0.6              0.1

- The expected value E(X) for the given random variable X is:

                E ( X ) = ∑Xi*P(Xi)

                           = 1*0.3 + 2*0.6 + 3*0.1

                           =1.8

- The variance Var(X) for the given random variable X is:

                Var ( X ) = ∑Xi^2*P(Xi) - [ E(X) ] ^2

                               = 1^2*0.3 + 2^2*0.6 + 3^2*0.1 - 1.8^2

                               = 0.36

- The standard deviation for the given random variable X is:

                σ = √Var(X)

                σ = √0.36

                σ = 0.6

5 0
3 years ago
17. The area of a rectangular sandbox is 8x2 + 18x + 9. If one of it's dimensions is (2x + 3), what is the other
Natasha2012 [34]

Answer:

The other dimension of the sandbox must be (4x+3).

Hope this helps! Have a good day!

6 0
2 years ago
1/4+3/8 and show work, please!!
gregori [183]

Answer:

The answer is 5/8

Step-by-step explanation:

Step 1 : Convert both fractions so they have the same denominator (bottom number in the fraction.)

1/4 = 2/8

So now were dealing with :

2/8 + 3/8 = ?

Step 2 : Add the numerators together to get the numerator for our answer.

2 + 3 = 5

When adding two fractions with the same denominator the denominator stays the same, so our answer is 5/8.

Hope this helps, please mark brainliest. :) Have a nice day.

7 0
2 years ago
Read 2 more answers
HELPPPP will mark brainliest
ArbitrLikvidat [17]

Answer:

12x-2

Step-by-step explanation:

You need to add 5x+1 and 7x-3.

5x+1+7x-3.

We need to organize this into common terms.

5x+7x+1-3

Now we simplify.

12x-2

That is the final answer!!

Hope this helped!!!! :D

6 0
3 years ago
How long will it take you to drive 175 miles at a speed of 25 miles per hour?
krek1111 [17]
I believe it would take you 7 hours at that miles per hour
6 0
3 years ago
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