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$You are dealt one card from a 52 -card deck. Find the probability that you are not dealt a card with number from 2 to 8. The probability is _____. (Type an integer or a simplified fraction.)$

You are dealt one card from a $52$ - card deck. Find the probability that you are not dealt a card with number from $2$ to $8$ . $\newline$ The probability is $\_\_\_\_\_$ . $\newline$ (Type an integer or a simplified fraction.)

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Find probabilities using the addition rule

Full solution

Q. You are dealt one card from a

52

- card deck. Find the probability that you are not dealt a card with number from

2

to

8

.

\newline

The probability is

\_\_\_\_\_

.

\newline

(Type an integer or a simplified fraction.)

Determine Total Cards: Let's first determine the total number of cards in a standard deck that have numbers from $2$ to $8$ . Each suit (hearts, diamonds, clubs, spades) has one card for each number from $2$ to $8$ , which makes $7$ cards per suit. Since there are $4$ suits, we have $7 \times 4 = 28$ cards with numbers from $2$ to $8$ .
Find Remaining Cards: Now, we need to find the number of cards that do not have numbers from $2$ to $8$ . Since there are $52$ cards in total and $28$ of these are from $2$ to $8$ , the remaining cards are $52 - 28 = 24$ .
Calculate Probability: The probability of an event is given by the number of favorable outcomes divided by the total number of possible outcomes. In this case, the favorable outcomes are the $24$ cards that are not numbered from $2$ to $8$ , and the total number of possible outcomes is the total number of cards, which is $52$ .
Calculate Probability: The probability of an event is given by the number of favorable outcomes divided by the total number of possible outcomes. In this case, the favorable outcomes are the $24$ cards that are not numbered from $2$ to $8$ , and the total number of possible outcomes is the total number of cards, which is $52$ .Calculating the probability, we have $P(\text{not } 2 \text{ to } 8) = \frac{24}{52}$ . This fraction can be simplified by dividing both the numerator and the denominator by $4$ , which gives us $P(\text{not } 2 \text{ to } 8) = \frac{6}{13}$ .

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