quantitative reasoning help

[savvysearch]

Hi, what is the probability of 6 tails of 9 tosses of a coin? A: 21/128

I tried binomial but that is impractical and takes forever. How did you guys do this problem?

Also, any way to evaluate 1/3 + 3/4 - 4/7 + 1/2 using clever shortcuts? Im trying desperately to cut my time calculating. a:73/84

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[Balki]

Hey,
savvysearch

I'll give you a general algorithm for doing the first problem.
The total Probabilty will be= Prbablity of the tosses happening x number rotations x probability it won't happen.
So
you want
TTTTTTHHH (right?)
But is also can be TTTTTHTHH see the difference? that's where the number of rotations come from. now let's do it
(1/2)^6 x (9!/ 6! x 3!) x (1/2)^3

the factorials are the number of rotations and it is 9C6 Let me know if you need any clarification on this. The answer should work out fine.

The fractions you can do a LCD and add them, then do a simple division to get the answer. If that's not good enough try combining one or two of the fractions and then doing the operation. This shouldn't take much time. What I would do is choose the LCD for everything at ounce.: first two fractions give you 3 and 4 => that's 12 and then you have a 7, So 7 times 12 = 84 =>that's your common dinaminator. Maybe you can pick the answer already, if not do the numerators and get the answer.

Wish you lots of luck.

 

[ShawnOne]

Balki,

The explaination you gave is correct, good job. But, I want the original poster to know that you WILL NOT have a problem that hard on the DAT. The statistics problems you are likely to encounter of the type:

3 red balls
2 green balls
5 yellow balls

whats the probability of selecting 2 green balls in a row?

or

How many seating arrangements can you have for you and 5 dinner guests?

I would recommend that you know the difference between the counting rule for permutations (order is important) and the combination rule (order not important).

Good luck

 

[savvysearch]

thanks for your help. I think Ill just have to do it the long way.

 

[critterbug]

Originally posted by ShawnOne
Balki,

The explaination you gave is correct, good job. But, I want the original poster to know that you WILL NOT have a problem that hard on the DAT. The statistics problems you are likely to encounter of the type:

3 red balls
2 green balls
5 yellow balls

whats the probability of selecting 2 green balls in a row?

or

How many seating arrangements can you have for you and 5 dinner guests?

I would recommend that you know the difference between the counting rule for permutations (order is important) and the combination rule (order not important).

Good luck

Shawn

Could you explain the counting rule vs combination rule or at least point me in the right direction to get a good explanation. On the Quant section, the probability questions give me the most trouble.

Thanks in advance,
critter

 

[Balki]

critterbug, this is for you. Two pages discussing differences between combinations and permutations. You most likely will be using Combinations(order doesn't matter) But you want to understand the difference click on the pages i think they provide sufficient information.
http://www.mathagonyaunt.co.uk/STATISTICS/ESP/Perms_combs.html
http://homepages.ius.edu/MEHRINGE/T102/Notes/Section7-5.htm


Good luck

 

[blankguy]

Originally posted by ShawnOne
Balki,

The explaination you gave is correct, good job. But, I want the original poster to know that you WILL NOT have a problem that hard on the DAT. The statistics problems you are likely to encounter of the type:

3 red balls
2 green balls
5 yellow balls

whats the probability of selecting 2 green balls in a row?

or

How many seating arrangements can you have for you and 5 dinner guests?

I would recommend that you know the difference between the counting rule for permutations (order is important) and the combination rule (order not important).

Good luck

I'm tempted to take a crack at this without looking at any math pages.
The first one is 1/10+1/9 since if I took out a green one(1/10th) chance of that we have 9 balls left so the last green(1/9th).
Or is it 1/10*1/9??

The second I guess is 5*5 for 25. Is this right?

 

[pkoneru]

Can anyone explain me how this type of questions can be cracked?

A Boat takes 4 hrs to travel a particular distance upstream and 3hrs downstream. If the speed of the boat is in still water is 4mph, what is the speed of the stream?

thank you

 

[Streetwolf]

Can anyone explain me how this type of questions can be cracked?

A Boat takes 4 hrs to travel a particular distance upstream and 3hrs downstream. If the speed of the boat is in still water is 4mph, what is the speed of the stream?

thank you

Start a new thread next time instead of bumping a 6 year old thread.

Speed of boat (b) = 4
Speed of stream = s (unknown)

Remember rate * time = distance

Rate upstream = b - s
Rate downstream = b + s

Since the distances are equal, you can set rate * time equal to each other for upstream and downstream.

Distance upstream = Distance downstream
Rate upstream * Time upstream = Rate downstream * Time downstream
(4-s) * 4 = (4 + s) * 3
16 - 4s = 12 + 3s
4 = 7s
s = 4/7 mph

Is this right?

Rate upstream is 4 - 4/7 = 24/7 mph
Rate downstream is 4 + 4/7 = 32/7 mph

Distance upstream is 24/7 * 4 = 96/7 miles
Distance downstream is 32/7 * 3 = 96/7 miles

So we're good.