Could anyone help me by checking my homework? Due tonight!

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June 28th 2010, 07:26 AM
rtn360

Could anyone help me by checking my homework? Due tonight!

Having trouble grasping these concepts. Any help would be greatly appreciated.

1) You are rolling a pair of 6 sided dice. Find the probabilities.

i) sum is greater than 5 on two rolls in a row.........i got the answer 13/18
j) sum is greater than 5 on either 1st or 2nd throw........i got the answer 169/324

2) Using a standard deck of 52 cards compute the following probabilities

a) at least 1 black card in a 5 card hand.....i got 65780
b) at least 1 face card in a 5 card hand.......i got 792
c) a flush in a 5 card hand.....i got 1287
d) a flush in a 7 card hand......i got 1716
3) from a standard deck of 52 cards, 1 card is drawn

a) find P(diamond|red). are these two independent? ........i got 1/4, dependent
b) find P(even|diamond) (assume face cards no value) are they independent......i got 1/8 independent
c) if you are playing a game where you win 100$ if your card is king. If the game is fair, how much should you loose if you do not draw a king?....i got $8.33
4) you flip 2 coins. you win $2 if the coins show the same side and you loose $3 if they show different sides. what is the expected value of this game. how much should you loose for the game to be fair?......i got $2

5) 5000 raffle tickets are sold at $1 for a charity raffle. The prizes being offered are: 1 prize of $500, 3 prizes o $100, 5 prizes of $20, and 20 prizes of$5. Construct a payout table. Calculate the expected value for purchasing one ticket.........i got -$0.82 per ticket

6) one of two urns is chosen at random with one as likely to be chosen as the other. Then a ball is withdrawn from the chosen urn. Urn 1 has 1 white and 4 red balls, and urn 2 has 3 white and 2 red balls.
a) if a white ball is drawn, what is the probability that it came from urn 1...i got 1/4
b) if a white ball is drawn, what is the probability that it came from urn 2...i got 3/4
c) if a red ball is drawn, what is the probability that it came from urn 1....i got 2/3
d) if a red ball is draw, what is the probability that it came form urn 2....i got 1/3

7.) Find the probability that a randomly chosen positive integer less than or equal to 1000 is divisible by 6 or 8...i got 1/4
June 28th 2010, 08:04 AM
Grandad

Hello rtn360

Quote:

Originally Posted by rtn360

Having trouble grasping these concepts. Any help would be greatly appreciated.

1) You are rolling a pair of 6 sided dice. Find the probabilities.
i) sum is greater than 5 on two rolls in a row.........i got the answer 13/18

No. Should be $\displaystyle\left(\frac{13}{18}\right)^2$

Quote:

j) sum is greater than 5 on either 1st or 2nd throw........i got the answer 169/324

No. Should be $\displaystyle2\times\frac{13}{18}\times\frac{5}{18 }$

Quote:

2) Using a standard deck of 52 cards compute the following probabilities
a) at least 1 black card in a 5 card hand.....i got 65780
b) at least 1 face card in a 5 card hand.......i got 792
c) a flush in a 5 card hand.....i got 1287
d) a flush in a 7 card hand......i got 1716

These answers don't make sense. A probability must have a value between 0 and 1.

For (a), work out the probability that all cards are red; then subtract the result from 1. This comes to 0.9747.

Quote:

3) from a standard deck of 52 cards, 1 card is drawn[INDENT] a) find P(diamond|red). are these two independent? ........i got 1/4, dependent

Yes, they are dependent - a card cannot be a diamond unless it is red. But P(diamond|red) means that you know that the card is red. So the probability that it's a diamond is $\frac12$ .

Quote:

b) find P(even|diamond) (assume face cards no value) are they independent......i got 1/8 independent

Yes they are independent. But, out of 13 cards, if face cards have no value (i.e. they are not even) there are 5 even cards. So the probability that a card drawn at random is even is $\frac{5}{13}$ .

Quote:

c) if you are playing a game where you win 100$ if your card is king. If the game is fair, how much should you loose if you do not draw a king?....i got $8.33

Correct. You are 12 times more likely not to draw a king than to draw one.

Maybe someone else will give you some help with the remaining questions.

Grandad
June 28th 2010, 08:12 AM
rtn360

Thanks Grandad for the quick response! Definitely a helping explanation for those questions.