Problem:
From a standard deck of 52 playing cards, one card is drawn at random, compute the probability of getting:
Solution:
In order to answer this word problem involving probability, we should know first the composition of a standard deck. There are 4 suites that can be found in the deck: club, spade, heart and diamond wherein the club and spade are in black while the heart and diamond are in red. There are 13 cards for each suite starting from the ace, two, three until ten from the number cards, and Jack, Queen and King for the face cards. So that's 10 plus 3.
Now, since we already know the basic composition of the standard deck, we can already answer the questions. Take note that in this case, the probability can be obtained by taking the total number of the random card available in the deck divided by the total number of playing cards which is 52.
For #1: Compute the probability of drawing an ace card.
Since there are 4 suites, the ace card is also available in all of the suites. It means that there are four ace cards that can be possibly drawn from the deck. Hence, the probability is 4/52. We can further simplify this fraction to its lowest term by dividing the numerator and denominator by its greatest common divisor which is 4. So, 4 divided by 4 is 1, and 52 divided by 4 is 13. This will reduce 4/52 into 1/13.
For #2: Compute the probability of drawing a non-face card.
There are 10 non-face cards in each suite. Since we have four suites, let us multiply 4 by 10 which will give us 40. Hence, the probability is 40/52. However, since 40/52 can still be reduced to its simplest form by dividing their GCD which is 4, so: 40 divided by 4 is 10 while 52 divided by 4 is 13. Thus, the probability is 10/13.
For #3: Compute the probability of drawing neither a spade nor a jack.
This means that we should get a card that is not a spade or a jack. We know the a suite is consist of 13 cards. Since the Jack of Spade is already counted in the spade suite, then we still have 3 more non-spade Jacks in the deck. Therefore, there are 13 plus 3 equals 16 spades and Jacks in a standard deck. Since we are getting the probability of neither a spade or Jack, we will subtract 16 from the total number of cards. This will give us: 52 - 16 = 36 cards. Then, we will divide this by 52. The resulting probability is 36/52. But, this can still be simplified by dividing 4 to both of them. 36 divided by 4 is 9 while 52 divided by 4 is 13. Therefore, the probability is 9/13.
How to solve for GCD using listing method? Click here: https://brainly.ph/question/12080834
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