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1.) a card is picked at random. find the probability of drawing card either a 4 or a face card?
2.) a two die is rolled. what is the probability of showing a prime number or a number divisible by 3?
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Answer:
1.) There are 52 cards in a standard deck of cards, of which there are 4 4's and 12 face cards (Jack, Queen, King of each suit).
The probability of drawing a 4 is 4/52, which reduces to 1/13.
The probability of drawing a face card is 12/52, which reduces to 3/13.
However, we need to be careful not to double-count the cards that are both 4's and face cards (i.e. the Jacks, Queens, and Kings of each suit). There are 3 of these in each suit, for a total of 12 cards, which we have already counted as face cards. So the total probability of drawing either a 4 or a face card is:
1/13 + 3/13 - 3/52 = 11/26, or approximately 0.4231.
Therefore, the probability of drawing either a 4 or a face card is 11/26.
2.) There are 6 possible outcomes when rolling two dice: (1,1), (1,2), (1,3), ..., (6,5), (6,6). Of these, the numbers that are prime are 2, 3, 5, and 7. The numbers that are divisible by 3 are 3 and 6.
To count the number of outcomes that are either prime or divisible by 3, we need to be careful not to double-count the outcomes that are both (i.e. the outcome (3,3)). There are:
- 10 outcomes that are prime, but not divisible by 3: (1,2), (1,4), (1,5), (2,1), (2,3), (2,5), (3,2), (3,4), (4,1), and (5,1).
- 7 outcomes that are divisible by 3, but not prime: (1,3), (2,3), (3,1), (3,2), (3,4), (4,3), and (5,3).
- 1 outcome that is both prime and divisible by 3: (3,3).
Therefore, there are 10 + 7 - 1 = 16 outcomes that are either prime or divisible by 3. Since there are 36 possible outcomes in total, the probability of rolling a prime number
Step-by-step explanation:
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