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Lapatulllka [165]
3 years ago
5

A standard deck of cards contains 52 cards. One card is selected from the deck. ​(a) Compute the probability of randomly selecti

ng a heart or diamond. ​(b) Compute the probability of randomly selecting a heart or diamond or spade. ​(c) Compute the probability of randomly selecting a ten or spade.
Mathematics
1 answer:
den301095 [7]3 years ago
3 0

Answer:

a) 0.5

b) 0.75

c) 0.307  

Step-by-step explanation:

We are given the following information in the question:

Number of cards in a deck = 52

Formula:

\text{Probability} = \displaystyle\frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}

a) P(Heart or Diamond)

Total number of hearts and diamonds in a deck = 13 + 13 = 26

P( Heart or Diamond) =

\displaystyle\frac{26}{52} = \displaystyle\frac{1}{2} = 0.5

b)  P(Heart or Diamond or Spade)

Total number of hearts, diamonds and spades in a deck = 13 + 13 + 13 = 39

P( Heart or Diamond or Spades) =

\displaystyle\frac{39}{52} = \displaystyle\frac{3}{4} = 0.75

c)  P(10 or Spades)

Total number of spades in a deck = 13

Number of 10 in a deck = 4

P( 10 or Spades) =

\displaystyle\frac{13 + 4 -1}{52} = \displaystyle\frac{16}{52} = \displaystyle\frac{4}{13} = 0.307

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Answer:

Part A) see the explanation

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Step-by-step explanation:

<u><em>The complete question is</em></u>

The isosceles trapezoids, ABCD and EFGH, are similar quadrilaterals. The scale factor between the trapezoids is 2:3, GH = 6 centimeters, AD = 8 centimeters, and AB is three times the length of DC

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The corresponding sides are

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we know that

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∠B ≅ ∠F

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The scale factor between the trapezoids is 2:3, GH = 6 centimeters, AD = 8 centimeters, and AB is three times the length of DC

step 1

Find the measure of CD

Remember that

The ratio between corresponding sides is proportional and this ratio is the scale factor

Let

z ----> the scale factor

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step 2

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step 3

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step 4

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substitute the values

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step 5

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we know that

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y ----> the perimeter of trapezoid EFGH

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z=\frac{2}{3}

x=32\ cm

substitute

\frac{2}{3}=\frac{32}{y}

y=32(3)/2=48\ cm

therefore

The perimeter of trapezoid EFGH is 48 centimeters

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