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 9
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Part 1
The probability is enter your response here
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(Type an integer or a simplified fraction.)
There are 36 cards in the deck that are not numbered from 2 to 9 (10, J, Q, K, and A of each suit). There are a total of 52 cards in the deck.
Therefore, the probability of not being dealt a card with a number from 2 to 9 is:
P(not being dealt a card with number from 2 to 9) = 36/52
Simplifying the fraction, we get:
P(not being dealt a card with number from 2 to 9) = 9/13
Simplify 9/13
The fraction 9/13 cannot be simplified any further because 9 and 13 do not have any common factors other than 1. Therefore, 9/13 is already in its simplified form.
please explain how there are 36 cards in the deck of 52 cards that are not numbered 2 through 9.
Apologies for the error in my previous response. You are correct that there are only 32 cards in a standard deck that are not numbered 2 through 9.
In a standard deck of 52 cards, there are 4 of each number card (2, 3, 4, 5, 6, 7, 8, and 9) for each suit (hearts, diamonds, clubs, and spades).
So, the total number of cards numbered 2 through 9 is 4 * 8 = 32.
The probability of not being dealt a card with a number from 2 to 9 can be found by subtracting the probability of being dealt such a card from 1 (since the probability of any event happening is 1 minus the probability of it not happening).
Therefore, the probability of not being dealt a card with a number from 2 to 9 is:
P(not being dealt a card with number from 2 to 9) = 1 - 32/52
Simplifying the fraction, we get:
P(not being dealt a card with number from 2 to 9) = 1 - 8/13
To subtract the fractions, we need a common denominator:
P(not being dealt a card with number from 2 to 9) = 13/13 - 8/13
P(not being dealt a card with number from 2 to 9) = 5/13
i don't get it. There are 32 cards from 2 through 9; therefore, there are 20 that are not numbered 2 through 9. 10, J, Q, K, A; i.e., 5 cards in each suit and 5 x 4 = 20 cards not numbered 2 through 9
Apologies for the confusion. You are correct, there are 32 cards numbered 2 through 9 (4 of each number 2, 3, 4, 5, 6, 7, 8, 9) in a deck of 52 cards.
Therefore, the number of cards in the deck that are not numbered 2 through 9 is 52 - 32 = 20.
The probability of not being dealt a card with a number from 2 to 9 is:
P(not being dealt a card with number from 2 to 9) = 20/52 = 5/13
So, the probability that you are not dealt a card with a number from 2 to 9 is 5/13.