Looking for help on a few problems for a test

[Jangoon]

Hey everybody, I have a worksheet to prepare for an upcoming test and I'm stumped on a few questions. I'll include where I currently stand on them and I'm just trying to make sure that I'm doing these right so I'm confident when I run into problems like this on the test:

1. Jeff has 6 different pairs of gloves in a drawer. If two gloves are chosen at random from the drawer, what is the probability that they will be a matched pair?

- Since the first glove pulled doesn't affect the probability, isn't this just 1/11 or .091?

2. Suppose your company work group has 10 members. What is the probability that you will be chosen to represent your group if:
a) one representative is chosen? b) two representatives are chosen?
- Isn't this 1/10 or .1? - I'm torn between 2/10 or .2 and 2/100 or .02 (not sure if either of these are correct)

3. In the state tournament, the Eagles have a 40% chance of winning, the Raptors have a 30% chance of winning, and the only other two teams (the Cardinals and Orioles) are equally likely to win. What is the probability that:
a) the Cardinals win? b) the Raptors DON'T win? c) either the Eagles or the Orioles win?
- 15% or .15? - 70% or .70? - 55% or .55?
(I'm questioning these because I don't think this problem is that easy or if I'm even doing this right at all)

4. If a fair six-sided die is rolled 5 times and the results of each roll are recorded, then how many recorded sequences end with 4, 6?
- I did 12*5 here to come up with 60?

5. What is the probability that exactly 3 sixes are recorded when 5 fair dice are thrown?
- I got 3.21% or .0321 here

6. What is the probability that exactly 3 clubs are showing then 5 cards are dealt from a 52-card deck?
- I did 13/52 * 3/5 here to get 15% or .15




Any help or guidance here would be fantastic and I'd greatly appreciate it. Thanks!

 

[DrPhil]

Hey everybody, I have a worksheet to prepare for an upcoming test and I'm stumped on a few questions. I'll include where I currently stand on them and I'm just trying to make sure that I'm doing these right so I'm confident when I run into problems like this on the test:

1. Jeff has 6 different pairs of gloves in a drawer. If two gloves are chosen at random from the drawer, what is the probability that they will be a matched pair?

- Since the first glove pulled doesn't affect the probability, isn't this just 1/11 or .091?....YES

2. Suppose your company work group has 10 members. What is the probability that you will be chosen to represent your group if:
a) one representative is chosen? b) two representatives are chosen?
- Isn't this 1/10 or .1? ....YES
- I'm torn between 2/10 or .2 and 2/100 or .02 (not sure if either of these are correct)..If you were already chosen first, then you cant be chosen 2nd as well. (1/10) + (9/10)(1/9) = 2/10

3. In the state tournament, the Eagles have a 40% chance of winning, the Raptors have a 30% chance of winning, and the only other two teams (the Cardinals and Orioles) are equally likely to win. What is the probability that:
a) the Cardinals win? b) the Raptors DON'T win? c) either the Eagles or the Orioles win?
- 15% or .15? - 70% or .70? - 55% or .55?....YES .. it is "easy" because the events are mutually exclusive
(I'm questioning these because I don't think this problem is that easy or if I'm even doing this right at all)

4. If a fair six-sided die is rolled 5 times and the results of each roll are recorded, then how many recorded sequences end with 4, 6?
- I did 12*5 here to come up with 60?.. We don't know total number of recorded sequences, so we have to answer as probability.
p(4th roll=4) = 1/6, p(5th roll=6) = 1/6, p(xxx46) = . . .

5. What is the probability that exactly 3 sixes are recorded when 5 fair dice are thrown?
- I got 3.21% or .0321 here....YES

6. What is the probability that exactly 3 clubs are showing then 5 cards are dealt from a 52-card deck?
- I did 13/52 * 3/5 here to get 15% or .15...NO

Any help or guidance here would be fantastic and I'd greatly appreciate it. Thanks!

#6. If the drawings were made with replacement, this would be similar to #5, but with p=1/4 instead of 1/6. That would give 8.8%. Without replacement, the probabilities decrease with each draw, so the answer has to be of the order 8% or so.

One possible sequence would be to draw 3 clubs followed by 2 not-clubs:
P(CCCxx) = (13/52)(12/51)(11/50)(39/49)(38/48) = 0.00815
Because of the combinations that can be made with those 5 cards, of which 3 are "indistinguishable," you multiply that one specific sequence by 5C3, giving a final result of 8.15%

Good luck on the test!

 

[Jangoon]

DrPhil, thank you so much for taking a look at my answers for me! I have a minor question with number 4 though; are you saying my answer is right since you used the green text, or am I to just follow the formula you included in the next line?

 

[DrPhil]

DrPhil, thank you so much for taking a look at my answers for me! I have a minor question with number 4 though; are you saying my answer is right since you used the green text, or am I to just follow the formula you included in the next line?

Do the next line - I wasn't completely color-coded.