QuestionWhat is the probability of drawing a King or an odd-valued card from a standard deck? Provide your answer as a fraction or decimal (3 decimal places).

Studdy Solution

STEP 1

Assumptions1. A standard deck of cards has52 cards4 suits of13 cards each (Ace through10, and the face cards Jack, Queen, King). . The13 cards include4 odd valued cards (Ace counted as1,3,5,7,9), and1 King.
3. The event of drawing a King and the event of drawing an odd valued card are mutually exclusive (a King is not an odd valued card).

STEP 2

First, we need to find the total number of favorable outcomes. This is the sum of the number of Kings and the number of odd valued cards in the deck.
$Number\,of\,favorable\,outcomes = Number\,of\,Kings + Number\,of\,odd\,valued\,cards$

STEP 3

Now, plug in the given values for the number of Kings and odd valued cards to calculate the number of favorable outcomes.
$Number\,of\,favorable\,outcomes = + \\times$

STEP 4

Calculate the number of favorable outcomes.
$Number\,of\,favorable\,outcomes =4 +4 \\times4 =20$

STEP 5

The probability of an event is the ratio of the number of favorable outcomes to the total number of outcomes. In this case, the total number of outcomes is the number of cards in the deck, which is52.
$Probability = Number\,of\,favorable\,outcomes / Total\,number\,of\,outcomes$

STEP 6

Plug in the values for the number of favorable outcomes and the total number of outcomes to calculate the probability.
$Probability =20 /52$

STEP 7

implify the fraction to its lowest terms.
$Probability =20 /52 =5 /13$ The probability of drawing a King or an odd valued card from a standard deck is5/13 or approximately0.385 when rounded to three decimal places.

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QuestionWhat is the probability of drawing a King or an odd-valued card from a standard deck? Provide your answer as a fraction or decimal (3 decimal places).

Studdy Solution

STEP 1

STEP 2

First, we need to find the total number of favorable outcomes. This is the sum of the number of Kings and the number of odd valued cards in the deck.
$Number\,of\,favorable\,outcomes = Number\,of\,Kings + Number\,of\,odd\,valued\,cards$

STEP 3

Now, plug in the given values for the number of Kings and odd valued cards to calculate the number of favorable outcomes.
$Number\,of\,favorable\,outcomes = + \\times$

STEP 4

Calculate the number of favorable outcomes.
$Number\,of\,favorable\,outcomes =4 +4 \\times4 =20$

STEP 5

The probability of an event is the ratio of the number of favorable outcomes to the total number of outcomes. In this case, the total number of outcomes is the number of cards in the deck, which is52.
$Probability = Number\,of\,favorable\,outcomes / Total\,number\,of\,outcomes$

STEP 6

Plug in the values for the number of favorable outcomes and the total number of outcomes to calculate the probability.
$Probability =20 /52$

STEP 7

implify the fraction to its lowest terms.
$Probability =20 /52 =5 /13$ The probability of drawing a King or an odd valued card from a standard deck is5/13 or approximately0.385 when rounded to three decimal places.

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QuestionWhat is the probability of drawing a King or an odd-valued card from a standard deck? Provide your answer as a fraction or decimal (3 decimal places).

Studdy Solution

STEP 1

STEP 2

STEP 3

Now, plug in the given values for the number of Kings and odd valued cards to calculate the number of favorable outcomes.Number of favorable outcomes=+timesNumber\,of\,favorable\,outcomes = + \\timesNumberoffavorableoutcomes=+times

STEP 4

Calculate the number of favorable outcomes.Number of favorable outcomes=4+4times4=20Number\,of\,favorable\,outcomes =4 +4 \\times4 =20Numberoffavorableoutcomes=4+4times4=20

STEP 5

STEP 6

Plug in the values for the number of favorable outcomes and the total number of outcomes to calculate the probability.Probability=20/52Probability =20 /52Probability=20/52

STEP 7

implify the fraction to its lowest terms.Probability=20/52=5/13Probability =20 /52 =5 /13Probability=20/52=5/13The probability of drawing a King or an odd valued card from a standard deck is5/13 or approximately0.385 when rounded to three decimal places.

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Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Now, plug in the given values for the number of Kings and odd valued cards to calculate the number of favorable outcomes.
$Number\,of\,favorable\,outcomes = + \\times$

Calculate the number of favorable outcomes.
$Number\,of\,favorable\,outcomes =4 +4 \\times4 =20$

Plug in the values for the number of favorable outcomes and the total number of outcomes to calculate the probability.
$Probability =20 /52$

implify the fraction to its lowest terms.
$Probability =20 /52 =5 /13$ The probability of drawing a King or an odd valued card from a standard deck is5/13 or approximately0.385 when rounded to three decimal places.