ok we got this packet that has an answer key and we g0tta show our work of how to get the answer. okayyy... they all seem like really easy problems s0 i think im just dumbbb

"a bag has 6 red and 2 white marbles. If two marbles are selected, what is the probability that one is red and the other is white?" - the answer is 3/7. how do i get that??

it seems like a real easy problem, i know. but i cant seem to get it :|

next. "Jose has 5 dimes, 7 nickels, and 4 pennies in his pocket. he selects 4 coins. What is the probability that he has 2 dimes and 2 pennies." -answer is 3/91.

Last one. "If a card is selected from a deck of cards, find the probability that it is not red or not a face card." answer is 23/26. This one really doesnt make sense ???

first one:

C(6,1)*C(2,1)/C8,2) = 6*2/28 = 3/7

second one:
C(5,2)*C(4,2)/C(16,4) = 10*6/1820 = 3/91

third one:

the key word is the "or"

prob(not red OR not a facecard)
= Prob(not red) + prob(not a facecard) - prob(not red AND not a facecard)
= 26/52 + 40/52 - 20/52
= 46/52
= 23/28

thank you so much!

To find the probabilities in these problems, we need to understand the concept of probability and how to count the favorable outcomes and total outcomes.

Let's start with the first problem:

"A bag has 6 red and 2 white marbles. If two marbles are selected, what is the probability that one is red and the other is white?"

To solve this, we need to calculate the favorable outcomes and the total outcomes.

Favorable outcomes: We want to select one red marble and one white marble. There are 6 red marbles and 2 white marbles. The first pick can be red and the second pick white, or vice versa. So, the favorable outcomes are 6 * 2 * 2 = 24.

Total outcomes: To calculate the total outcomes, we need to consider all possible combinations of picking 2 marbles from the bag that contains 8 marbles. The total outcomes can be calculated using the combination formula: "nCr" = n! / (r! * (n-r)!), where n is the total number of items and r is the number of items being chosen.

In this case, we have 8 marbles, and we are choosing 2. Therefore, the total outcomes are calculated as 8! / (2! * (8-2)!) = 8! / (2! * 6!) = (8 * 7) / 2 = 28.

Probability: The probability is the ratio of favorable outcomes to total outcomes. So, the probability is 24/28, which simplifies to 3/7.

Now let's move on to the second problem:

"Jose has 5 dimes, 7 nickels, and 4 pennies in his pocket. He selects 4 coins. What is the probability that he has 2 dimes and 2 pennies?"

To solve this, we need to again calculate the favorable outcomes and the total outcomes.

Favorable outcomes: We want to select 2 dimes and 2 pennies. There are 5 dimes and 4 pennies available. The favorable outcomes can be calculated as 5C2 * 4C2 = (5! / (2! * (5-2)!) * 4! / (2! * (4-2)!)) = 10 * 6 = 60.

Total outcomes: To calculate the total outcomes, we need to consider all possible combinations of picking 4 coins from the given set of 5 dimes, 7 nickels, and 4 pennies. The total outcomes can be calculated using the combination formula.

In this case, we have a total of 16 coins (5 dimes + 7 nickels + 4 pennies), and we are choosing 4 coins. Therefore, the total outcomes are calculated as 16! / (4! * (16-4)!) = 16! / (4! * 12!) = (16 * 15 * 14 * 13) / (4 * 3 * 2) = 56 * 13 = 728.

Probability: The probability is the ratio of favorable outcomes to total outcomes. So, the probability is 60/728, which simplifies to 3/91.

Lastly, let's address the third problem:

"If a card is selected from a deck of cards, find the probability that it is not red or not a face card."

To solve this problem, we need to calculate the favorable outcomes and total outcomes.

Favorable outcomes: We want to select a card that is not red or not a face card. There are two red suits (Hearts and Diamonds) and three face cards in each suit. So, we have (2 * 3) = 6 favorable outcomes.

Total outcomes: In a standard deck of 52 cards, there are 26 black cards (Clubs and Spades) and 12 face cards (King, Queen, Jack) (3 face cards * 4 suits = 12). So, there are 26 + 12 = 38 favorable outcomes.

Probability: The probability is the ratio of favorable outcomes to total outcomes. So, the probability is 38/52, which simplifies to 19/26.

I hope this explanation helps you understand how to solve these probability problems. If you have any further questions or need more clarification, please feel free to ask!