Math

QuestionA standard deck has 52 cards. Find the probability of choosing a 7:
Total cards = 52; Cards in event A = 4.
P(A)=452P(A) = \frac{4}{52}.

Studdy Solution

STEP 1

Assumptions1. The total number of cards in the deck is52. . There are four7's in the deck (one of each suit hearts, diamonds, clubs, spades).
3. Event AA is choosing a7 out of the deck of cards.

STEP 2

First, we need to identify the total number of outcomes in the sample space. This is simply the total number of cards in the deck.
Totaloutcomes=Totalnumberofcards=52Total\, outcomes = Total\, number\, of\, cards =52

STEP 3

Next, we need to identify the number of outcomes in event AA. This is the number of7's in the deck.
OutcomesineventA=Numberof7s=Outcomes\, in\, event\, A = Number\, of\,7's =

STEP 4

Now, we can calculate the probability of event AA. The probability of an event is the ratio of the number of outcomes in the event to the total number of outcomes in the sample space.
(A)=OutcomesineventATotaloutcomes(A) = \frac{Outcomes\, in\, event\, A}{Total\, outcomes}

STEP 5

Plug in the values for the outcomes in event AA and the total outcomes to calculate the probability.
(A)=452(A) = \frac{4}{52}

STEP 6

implify the fraction to its lowest terms.
(A)=113(A) = \frac{1}{13}So, there are52 cards in the sample space,4 cards in event AA, and the probability that you choose a out of the deck of cards is 113\frac{1}{13}.

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