Math / Data & Statistics

QuestionWe have a deck of 8 cards numbered from 1 to 8 . Some are white and some are grey, as shown below. 12 34
5 6 7 8
The cards numbered $1,4,6$ , and 8 are white. The cards numbered $2,3,5$ , and 7 are grey. Answer the following questions. Write each answer as a fraction.
A card will be drawn at random. (a) What is the probability that the card drawn is grey? $\square$ (b) What is the probability that the card drawn is grey, given that an evennumbered card is drawn? $\square$

Studdy Solution

STEP 1

1. There are 8 cards in total, numbered from 1 to 8.
2. Cards numbered 1, 4, 6, and 8 are white.
3. Cards numbered 2, 3, 5, and 7 are grey.
4. Probability is calculated as the number of favorable outcomes divided by the total number of possible outcomes.

STEP 2

1. Calculate the probability that the card drawn is grey.
2. Calculate the probability that the card drawn is grey, given that an even-numbered card is drawn.

STEP 3

Determine the total number of cards:
$8$

STEP 4

Determine the number of grey cards:
$4$

STEP 5

Calculate the probability that the card drawn is grey:
$\text{Probability} = \frac{\text{Number of grey cards}}{\text{Total number of cards}} = \frac{4}{8} = \frac{1}{2}$

STEP 6

Identify the even-numbered cards:
$2, 4, 6, 8$

STEP 7

Determine the number of even-numbered grey cards:
$1$ \quad (\text{Only card number 2 is grey and even})

STEP 8

Calculate the probability that the card drawn is grey, given that an even-numbered card is drawn:
$\text{Probability} = \frac{\text{Number of grey and even cards}}{\text{Total number of even cards}} = \frac{1}{4}$
The probabilities are: (a) $\frac{1}{2}$ (b) $\frac{1}{4}$

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Studdy Solution

STEP 1

1. There are 8 cards in total, numbered from 1 to 8.
2. Cards numbered 1, 4, 6, and 8 are white.
3. Cards numbered 2, 3, 5, and 7 are grey.
4. Probability is calculated as the number of favorable outcomes divided by the total number of possible outcomes.

STEP 2

1. Calculate the probability that the card drawn is grey.
2. Calculate the probability that the card drawn is grey, given that an even-numbered card is drawn.

STEP 3

Determine the total number of cards:
$8$

STEP 4

Determine the number of grey cards:
$4$

STEP 5

Calculate the probability that the card drawn is grey:
$\text{Probability} = \frac{\text{Number of grey cards}}{\text{Total number of cards}} = \frac{4}{8} = \frac{1}{2}$

STEP 6

Identify the even-numbered cards:
$2, 4, 6, 8$

STEP 7

Determine the number of even-numbered grey cards:
$1$ \quad (\text{Only card number 2 is grey and even})

STEP 8

Calculate the probability that the card drawn is grey, given that an even-numbered card is drawn:
$\text{Probability} = \frac{\text{Number of grey and even cards}}{\text{Total number of even cards}} = \frac{1}{4}$
The probabilities are: (a) $\frac{1}{2}$ (b) $\frac{1}{4}$

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Studdy Solution

STEP 1

1. There are 8 cards in total, numbered from 1 to 8.2. Cards numbered 1, 4, 6, and 8 are white.3. Cards numbered 2, 3, 5, and 7 are grey.4. Probability is calculated as the number of favorable outcomes divided by the total number of possible outcomes.

STEP 2

1. Calculate the probability that the card drawn is grey.2. Calculate the probability that the card drawn is grey, given that an even-numbered card is drawn.

STEP 3

Determine the total number of cards:8 8 8

STEP 4

Determine the number of grey cards:4 4 4

STEP 5

Calculate the probability that the card drawn is grey:Probability=Number of grey cardsTotal number of cards=48=12\text{Probability} = \frac{\text{Number of grey cards}}{\text{Total number of cards}} = \frac{4}{8} = \frac{1}{2}Probability=Total number of cardsNumber of grey cards​=84​=21​

STEP 6

Identify the even-numbered cards:2,4,6,8 2, 4, 6, 8 2,4,6,8

STEP 7

Determine the number of even-numbered grey cards:1 1 1 \quad (\text{Only card number 2 is grey and even})

STEP 8

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1. There are 8 cards in total, numbered from 1 to 8.
2. Cards numbered 1, 4, 6, and 8 are white.
3. Cards numbered 2, 3, 5, and 7 are grey.
4. Probability is calculated as the number of favorable outcomes divided by the total number of possible outcomes.

1. Calculate the probability that the card drawn is grey.
2. Calculate the probability that the card drawn is grey, given that an even-numbered card is drawn.

Determine the total number of cards:
$8$

Determine the number of grey cards:
$4$

Calculate the probability that the card drawn is grey:
$\text{Probability} = \frac{\text{Number of grey cards}}{\text{Total number of cards}} = \frac{4}{8} = \frac{1}{2}$

Identify the even-numbered cards:
$2, 4, 6, 8$

Determine the number of even-numbered grey cards:
$1$ \quad (\text{Only card number 2 is grey and even})