Matt and Dakota were playing a card game with 2 groups of diamonds. In the
first group were number cards: 2, 3, 4, 5, and 6. In the second group were face
cards: King, Queen, and Jack. Matt wins with an even card AND King. Dakota wins
with an odd card AND Queen or Jack.
1. Create a probability table or tree to show all outcomes of drawing a card
from each group.
2. What is the probability of Matt winning? What is the probability of Dakota
winning?
3. What is the probability of Matt not winning?
4. Is this a fair game? Why or why not?
5. If they play 45 rounds, how many times should Matt win?
6. In a new version of the game, Matt and Dakota play with both diamonds and hearts. If the rules stay the same, what is the probability of Dakota winning?
very confusing post
What are the rules?
"Matt wins with an even card AND King" ???
- are there cards drawn? how many cards ?
since your mention "2 groups of diamonds", there must be at least 2 decks
who holds the decks?
????? ... ????
"What are the rules?" there are no rules if u read it correctly u will get the answers right and know them
1. I cant di it on here bc I have to draw it
2. P(Matt wins) 3/15=1/5 P(Dakota wins) 4/15 P= probability
3. no, because there is not an equal chance of winning for Dakota nd Matt.
And haven't gotten to the rest
Hope this helps a little
Thx really helpful
To answer these questions, we will create a probability table to show all the outcomes of drawing a card from each group.
1. Probability Table:
Group 1 (Number cards): 2, 3, 4, 5, 6
Group 2 (Face cards): King, Queen, Jack
To create the probability table, we need to calculate the probability of each outcome by dividing the number of favorable outcomes by the total number of possible outcomes.
Group 1:
- Probability of drawing an even card = 3/5 (2, 4, 6 are even; 3, 5 are odd)
- Probability of drawing an odd card = 2/5 (3, 5 are odd; 2, 4, 6 are even)
Group 2:
- Probability of drawing a King = 1/3 (1 King out of 3 face cards)
- Probability of drawing a Queen = 1/3 (1 Queen out of 3 face cards)
- Probability of drawing a Jack = 1/3 (1 Jack out of 3 face cards)
Now we can combine the probabilities to get the outcomes:
- Matt wins with an even card AND King = (3/5) * (1/3) = 1/5
- Dakota wins with an odd card AND Queen or Jack = (2/5) * (1/3 + 1/3) = 4/15
2. The probability of Matt winning is 1/5, and the probability of Dakota winning is 4/15.
3. To find the probability of Matt not winning, we need to subtract the probability of Matt winning from 1:
Probability of Matt not winning = 1 - Probability of Matt winning
= 1 - 1/5
= 4/5
4. To determine if this is a fair game, we need to compare the probabilities of Matt and Dakota winning. In a fair game, the probabilities of all outcomes should be equal. In this case, the probabilities of Matt and Dakota winning are different (1/5 vs. 4/15), so it is not a fair game.
5. If they play 45 rounds, we can multiply the probability of Matt winning by the number of rounds to estimate the number of times Matt should win:
Number of times Matt should win = Probability of Matt winning * Number of rounds
= (1/5) * 45
= 9
Hence, Matt should win approximately 9 times if they play 45 rounds.
6. In the new version of the game with both diamonds and hearts, assuming the rules stay the same, the only change is that the total number of cards in each group has increased. Since we are interested in the probability of Dakota winning, we can ignore the probability of drawing diamonds.
Group 1 (Number cards): 2, 3, 4, 5, 6
Group 2 (Face cards): King, Queen, Jack
Now, to calculate the probability of Dakota winning, we need to determine the favorable outcomes.
Group 1:
- Probability of drawing an odd card = 2/5 (3, 5 are odd; 2, 4, 6 are even)
Group 2:
- Probability of drawing a Queen = 1/4 (1 Queen out of 4 face cards)
- Probability of drawing a Jack = 1/4 (1 Jack out of 4 face cards)
Dakota wins with an odd card AND Queen or Jack = (2/5) * (1/4 + 1/4) = 2/10 = 1/5
Therefore, in the new version of the game, the probability of Dakota winning is 1/5.