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Hitman42 [59]
3 years ago
13

A deck of cards with four suits; hearts, diamonds, spades, and clubs. you pick one card, put it back and thennpick another card.

what is the probability that the first card is a diamond and the second card is not a diamond
Mathematics
1 answer:
Llana [10]3 years ago
7 0

1. First, let us find the probability that the first card is a diamond.

Now, since we are given that there are four suits and there are, assumably, an equal number of cards in each suit, we can say that the probability of choosing a diamond card is 1/4. We can also write this out as such, where D = Diamond:

Pr(D) = no. of diamond cards / total number of cards

There are 52 cards in a deck, and 13 cards of each suit, thus:

Pr(D) = 13/52 = 1/4

2. Now we need to calculate the probability of not choosing a diamond as the second card.

In many cases, when given a problem that requires you to find the probability of something not happening, it may be easier to set it out as such:

Pr(A') = 1 - Pr(A)

ie. Pr(A not happening, or not A) = 1 - Pr(A happening, or A)

This works because the total probability is always 1 (100%), and it makes sense that to find the probability of A not happening, we take the total probability and subtract the probability of A actually happening.

Thus, given that we have already calculated that the probability of choosing a Diamond is 1/4, we can now set this out as such:

Pr(D') = 1 - Pr(D)

Pr(D') = 1 - 1/4

Pr(D') = 3/4

3. Now we come to the final step. To find the probability of something and then something else happening, we must multiply the two probabilities together. Thus, given that Pr(D) = 1/4 and Pr(D') = 3/4, we get:

Pr(D)*Pr(D') = (1/4)*(3/4)

= 3/16

Thus, the probability of choosing a diamond as the first card and then not choosing a diamond as the second card is 3/16.

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2 years ago
Given f (X) = 4x +6 find f (x) = 54
Nikitich [7]

Answer:

x = 12

Step-by-step explanation:

Step 1: Define

f(x) = 4x + 6

f(x) = 54

Step 2: Substitute variables

54 = 4x + 6

Step 3: Solve for <em>x</em>

<u>Subtract 6 on both sides:</u> 48 = 4x

<u>Divide both sides by 4:</u> 12 = x

Step 4: Check

<em>Plug in x to verify it is a solution.</em>

f(12) = 4(12) + 6

f(12) = 48 + 6

f(12) = 54

3 0
3 years ago
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More is coming but help help help #10 points
vovangra [49]

Answer:

Its the last one

Step-by-step explanation:

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It not much information because its hard to explain but,hope this helps!!!.

6 0
3 years ago
Justify each step in solving the equation -3(2x-3)=25-8x by writing a reason for each statement.
Mice21 [21]

Answer: x= 8.


Step-by-step explanation: Given equation -3(2x-3)=25-8x.

Step 1: We have -3 in front of (2x-3). We always simplify a parenthesis first.

Therefore, applying Distributive property in first step, we get

-6x +9 = 25-8x.

Step 2:  We need to get rid 9 from left side to get constant numbers on right side.

9 is being added on left side.

So, we would apply reverse operation of addition.

Therefore, applying Subtraction property of equality, we get

-6x +9-9 = 25-8x-9

-6x =16 -8x.

Step 3: We need to get rid 8x from right side.

The reverse operation of subtraction is addition.

Therefore, applying Addition property of equality, we get

-6x+8x =16 -8x+8x

2x = 16.

Step 4: We need to isolate it for x.

So, applying Division property of equality, we get

\frac{2x}{2}=\frac{16}{2}

<h3>x= 8.</h3>
4 0
3 years ago
in a certain chemical, the ratio if zinc to copper is 3 to 16. a jar of the chemical contains 320 grams of copper. how many gram
Dennis_Churaev [7]

Answer:

60 grams

Step-by-step explanation:

For these type of questions, we can equate the ratio with the actual amounts. We will let the quantity to find be an unknown variable, such as x. Then we equate the ratios, cross multiply, and use algebra to solve.

Let grams of zinc be "x", so we can write the ratios and actual amounts as:

\frac{3}{16}=\frac{x}{320}

Then we cross multiply and solve for x, what we want to find out. Shown below:

\frac{3}{16}=\frac{x}{320}\\16x =3 * 320\\16x = 960\\x = \frac{960}{16}\\x=60

There are 60 grams of zinc.

5 0
3 years ago
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