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Probability and Chance

Featured Replies

A die is rolled 10 times. Find the chances of --

 

a) getting 10 sixes

'B) not getting 10 sixes

c) all the rolls showing 5 spots or less

 

______________________________________________

 

One ticket will be drawn at random from each of the two boxes shown below:

 

(A) 1 2 3 ('B) 1 2 3 4

 

Find the chance that-

 

a) The number drawn from A is larger than the one from B

'B) The number drawn from A equals the one from B

c) The number drawn from A is smaller than the one from B

 

________________________________________________

 

Three cards are dealt from a well-shuffled deck.

 

a) Find the chance that all of the cards are diamonds

'B) Find the chance that none of the cards are diamonds

c) Find the chance that the cards are not all diamonds

 

 

Any help please!!! :huh

A die is rolled 10 times. Find the chances of --

 

a) getting 10 sixes

'B) not getting 10 sixes

c) all the rolls showing 5 spots or less

 

...ok. The odds of getting the first 6 are obviously 1/6. The odds of getting it the second time are still 1/6. So getting two sixes is (1/6)(1/6) = 1/36...and so on.

 

Part b is a gimme as soon as you get part a.

 

Part c is simple.

 

One ticket will be drawn at random from each of the two boxes shown below:

 

(A) 1 2 3 ('B) 1 2 3 4

 

Find the chance that-

 

a) The number drawn from A is larger than the one from B

'B) The number drawn from A equals the one from B

c) The number drawn from A is smaller than the one from B

 

Just write out every possibility.

A1 vs B1

A1 vs B2

...

A3 vs B3

 

Then determine how many of them fit the conditions.

 

Three cards are dealt from a well-shuffled deck.

 

a) Find the chance that all of the cards are diamonds

'B) Find the chance that none of the cards are diamonds

c) Find the chance that the cards are not all diamonds

 

This one is tougher, but you just have to know that diamonds are 13/52 cards. If one gets picked, then diamonds are 12/51 cards. If not, diamonds are 13/51 cards.

I'll give it a shot --- My name is the Cheat so I'm copying off of the asian kid.

 

A die is rolled 10 times. Find the chances of --

 

a) getting 10 sixes = (1/6)^10

'B) not getting 10 sixes = (5/6)^10

c) all the rolls showing 5 spots or less = (5/6)^10 -- I think

 

______________________________________________

 

One ticket will be drawn at random from each of the two boxes shown below:

 

(A) 1 2 3 ('B) 1 2 3 4

 

Find the chance that-

 

a) The number drawn from A is larger than the one from B

'B) The number drawn from A equals the one from B

c) The number drawn from A is smaller than the one from B

 

________________________________________________

 

Three cards are dealt from a well-shuffled deck.

 

a) Find the chance that all of the cards are diamonds = (1/4)*(12/51)*(11/50)

'B) Find the chance that none of the cards are diamonds = (39/52)*(38/51)*(37/50)

c) Find the chance that the cards are not all diamonds = (3/4)*(38/51)

 

 

The second group of questions has me stumped..

a) getting 10 sixes = (1/6)^10

'B) not getting 10 sixes = (5/6)^10

 

Cheat, the question was 'not getting 10 sixes', so getting 9 sixes is still good.

The answer is 1 - part a.

Cheat, the question was 'not getting 10 sixes', so getting 9 sixes is still good.

The answer is 1 - part a.

you're right... I was distracted by the hot, yet surprisingly unintelligent cheerleader next to me.

 

generalizations>

  • Author
...ok.  The odds of getting the first 6 are obviously 1/6.  The odds of getting it the second time are still 1/6.  So getting two sixes is (1/6)(1/6) = 1/36...and so on. 

 

Part b is a gimme as soon as you get part a.

 

Part c is simple.

So you are saying:

 

a) (1/6)^10

'B) (1/6)^10

c) (5/6)^10

a) (1/6)^10

'B) (1/6)^10

c) (5/6)^10

 

No.

So you are saying:

 

a) (1/6)^10

'B) (1/6)^10

c) (5/6)^10

B ) = 1 - (1/6)^10

  • Author
B ) = 1 - (1/6)^10

And why is that?

  • Author
Just write out every possibility.

A1 vs B1

A1 vs B2

...

A3 vs B3

 

Then determine how many of them fit the conditions.

a ) 1/4

b ) 1/4

c ) 1/2

part a is the probability that a 6 comes up 10 times in a row....

 

part b asks for the probability that a 6 doesn't come up 10 times in a row... It can come up 9 times however.

 

1 represents an assured event, i.e the likelyhood that a 2 headed coin lands on heads... or in the case of a die landing on any number.

 

The only roll that wouldn't make it a sure thing would be 10 6's in a row. Since you already know the probability of that event(part a), and the probability of an assured event, you can subtract part a from 1 to obtain the answer for part b

  • Author
part a is the probability that a 6 comes up 10 times in a row....

 

part b asks for the probability that a 6 doesn't come up 10 times in a row...  It can come up 9 times however.

 

1 represents an assured event, i.e the likelyhood that a 2 headed coin lands on heads... or in the case of a die landing on any number.

 

The only roll that wouldn't make it a sure thing would be 10 6's in a row.  Since you already know the probability of that event(part a), and the probability of an assured event, you can subtract part a from 1 to obtain the answer for part b

Got it! ;)

 

Thanks Cheat and Crimson for your help!!! :notworthy

 

BTW, does my answer for the second question look correct?

BTW, does my answer for the second question look correct?

EDIT>>>>>>>>

 

i'm dumb.... You're smart.... You got em right

I'll give it a shot --- My name is the Cheat so I'm copying off of the asian kid.

:lolhitting

A die is rolled 10 times.  Find the chances of --

 

a) getting 10 sixes

'B) not getting 10 sixes

c) all the rolls showing 5 spots or less

 

______________________________________________

 

One ticket will be drawn at random from each of the two boxes shown below:

 

(A)  1  2  3        ('B)  1  2  3  4

 

Find the chance that-

 

a) The number drawn from A is larger than the one from B

'B) The number drawn from A equals the one from B

c) The number drawn from A is smaller than the one from B

 

________________________________________________

 

Three cards are dealt from a well-shuffled deck.

 

a) Find the chance that all of the cards are diamonds

'B) Find the chance that none of the cards are diamonds

c) Find the chance that the cards are not all diamonds

 

 

Any help please!!! :huh

:finger :lol:

ah, i'm taking a Probability Theory II class right now (Stat major), i would have helped had i seen this.

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