please help me with my homework!?

Question

hey there! im having problems with my maths homework- we are doing probability the only thing is im not very good with cards so i cant quite finish 3 questions out of 50 will anyone help me with:
the probability as a fraction of:

drawing a king from a pack of cards,

throwing a prime number with a dice,

throwing a black king from a pack of cards.

thanks a lot!xxxx

Answer 1

There are 4 kings in a pack of 52 cards, so the probablility of getting any one of these is 4/52 = 1/13.

Of the 6 possible numbers to throw on a standard dice, three of them are prime (2, 3, and 5 -- typically 1 is NOT thought to be prime). Therefore, the probablility is simply equal to 3/6 = 1/2.

Of the 4 kings in a pack of 52 cards, 2 of them are black while 2 are red. Therefore, the probability of drawing a black king is equal to 2/52 = 1/26.

Answer 2

4 kings in a deck = 4 of 52 chances to draw a king from the deck

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When you throw 2 dice there are 12 possible outcomes 1,2,3,4,5,6,7,8,9,10,11 and12. The probability of a given number is equal to the number of ways you can get it divided by the total number of ways for all outcomes.

If you thought the answer was a 1 in 12 chance of a given outcome, think about this; there is clearly less chance of a 2 being thrown than an 8. This is because there is only one way to throw a 2 (throwing two 1s) but there are six ways to throw an 8; you can roll:

a 1 on the first die and a 6 on the second
a 2 on the first die and a 5 on the second
a 3 on the first die and a 4 on the second
a 4 on the first die and a 3 on the second
a 5 on the first die and a 2 on the second or
a 6 on the first die and a 1 on the second

There are five prime nunbers between 2 and 12; 2,3,5,7 and 11. You can work out the possible number of ways to throw each of these numbers in a similar way to above

For 2: There is only one way: 1 on the first die, 1 on the second

For 3: There are two ways: 1 on the first die and a 2 on the second or a 2 on the first die and a 1 on the second.

For 5: There are 4 ways: 1 on the first die and a 4 on the second, or a 2 on the first and a 3 on the second, or a 3 on the first and a 2 on the second, or a 4 on the first and a 1 on the second.

For 7: There are 6 ways: a 1 on the first and a 6 on the second, or a 2 on the first and a 5 on the second, or a 3 on the first and a 4 on the second, or a 4 on the first and a 3 on the second, or a 5 on the first and a 2 on the second, or a 6 on the first and a 1 on the second.

For 11: There are 2 ways: a 5 on the first and a 6 on the second or a 6 on the first and a 5 on the second.

So, you can add up the total number of possible ways to throw a prime number:
2 has 1 way
3 has 2 ways
5 has 4 ways
7 has 6 ways
11 has 2 ways

1+2+4+6+2 = 15

The total number of possible outcomes from two dice is 36 ways (there are 3 possible ways for 4, 5 ways for 6, 5 for 8, 4 for 9, 3 for 10 and 1 for 12, I’ll leave you to find the permutations for the non-prime numbers yourself). To calculate the probability of each outcome, take the number of ways for that outcome divided by the total number of ways (36).

So, the probability of throwing a prime number with two dice is 15/36.

To check, you can calculate the probability for each individual number.
2 has a probability of 1/36 (one possible way out of 36 total possible ways)
3 has a probability of 2/36
5 has a probability of 4/36
7 has a probability of 6/36
11 has a probability of 2/36

1+2+4+6+2 = 15

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2 Black kings in a deck = 2 of 52 chances of throwing a black king from the deck.

Answer 3

There are 52 cards in a deck and 4 kings, so the probability of drawing a king is 4/52, or 1/13. The probability of drawing a black king would be 1/2 of that, or 1/26.

On a 6-sided die, there are 3 prime numbers (2, 3, and 5). As a result, the probability of rolling a prime number would be 3/6, or 1/2.

Answer 4

drawing a king from a pack of cards
4/52 = 1/13

throwing a prime number with a dice
1, 2, 3, and 5 are primes so 4/6 = 2/3
(Note: C-Wryte is right. 1 is not considered to be a prime so the correct answer is 3/6 = 1/2)

throwing a black king from a pack of cards.
2/52 = 1/26

Answer 5

With most probability one needs to know the total possible outcomes: in a deck of cards it is 52; since there are four kings, hearts, clubs, spades and diamonds, the fraction becomes 4/52 or 1/13 or one to thirteen. Not sure if you mean a die or two die (dice) one die has six possibilities; a prime number is a number divisible by only one and itself , 2,3,5. sowith one die the fraction becomes 3/6 , 1/2 , or one to two (1:2) There are two black kings and 52 cards, hence, 2/52 or 1/26 hope it helps.

Answer 6

well i have done this a long time ago but i will try to help
u got a 4 out of 52 probability (1 out of 13) to get a king from a pack of cards (if you use a 52 card deck with 4 kings)
4 out of 6 (2 out of 3) to get a prime since u have 6 different numbers and 1,2,3,5 are primes
u got a 2 out of 52 (1 out of 26) to get a king from a pack of cards (if you use a 52 card deck with 2 black kings)

hope this helps!

Answer 7

4/52 = 1/13 [4 kings, 52 cards]

3 prime nunbers (2,3,5), and 6 possible numbers
So probability = 3/6 =1/2

2 Black Kings
Thus 2/52 = 1/26

Answer 8

1.) There are 4 kings and 52 cards so 4/52
2.) There are 3 prime numbers (1,3,5) out of 6 numbers, so 3/6

3.) There a 2 black kings and 52 card, so 2/52

Answer 9

A deck of cards has 52 cards

There are four kings (one of each suit) in a deck.
So, 4/52 or 1/13

A die has six sides, 1-6. The primes are 1,2,3,5.
So, 4/6 or 2/3

There are two black kings (spades and clubs) in a deck.
So, 2/52 or 1/26

Answer 10

king from deck 1/13
throwing prime number 1/2
a black king 1/26