probability

[tRNA]

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1) A six sided die is thrown twice. What is the probability that both the sum and the product of the two numbers thrown will be odd?
my guess is 3/6 x3/6= 9/36=1/4

2) A six sided die is thrown twice. What is the probability that the sum or the product of the two numbers thrown will be odd ?

3) A six sided die is thrown twice. What is the probability that the sum or the product of the two numbers thrown will be even ?

I know the word "and" in probability means multiplication and the word "or" in probability means addition...but is that always true?? and if it is I don't know what to add or multiply in these problems
plz don't reduce your intermediate steps until the end, it helps me understand better thanks

2nd Request: I did the QR and RC problems at the end of kaplan's lesson book pg 328-355 but unfortunately I don't have the right answers for any of them since my course expired before i get to that part so i don't even know how i did.....if anyone has the correct answers to these pleeeez post them, just if it's a,b,c,...
I am sure others will benefit too

thanks alot

 

[Streetwolf]

1) A six sided die is thrown twice. What is the probability that both the sum and the product of the two numbers thrown will be odd?
my guess is 3/6 x3/6= 9/36=1/4

2) A six sided die is thrown twice. What is the probability that the sum or the product of the two numbers thrown will be odd ?

3) A six sided die is thrown twice. What is the probability that the sum or the product of the two numbers thrown will be even ?

1) Sum is odd when one number is odd and one number is even. Product is odd when both numbers are odd. Thus the probability is 0.

2) The only way the sum or product won't be odd is if both numbers are even. The odds of this happening with die 1 is 3/6. Same for die 2, 3/6. So the odds are 3/6 x 3/6 = 1/4 *edit: for both numbers being even. To find the desired probability you need to take 1 - 1/4 = 3/4.*

3) Sum OR product even is the same as the probability that the sum AND product is NOT odd. (Why?) We know that the probability that the sum and product both odd is 0. So the probability that this ISN'T the case is just 1 - 0 = 1. Thus the probability that the sum or product is even is 1. It will always happen.

 

[nanaschool2000]

1) Sum is odd when one number is odd and one number is even. Product is odd when both numbers are odd. Thus the probability is 0.

2) The only way the sum or product won't be odd is if both numbers are even. The odds of this happening with die 1 is 3/6. Same for die 2, 3/6. So the odds are 3/6 x 3/6 = 1/4.

3) Sum OR product even is the same as the probability that the sum AND product is NOT odd. (Why?) We know that the probability that the sum and product both odd is 0. So the probability that this ISN'T the case is just 1 - 0 = 1. Thus the probability that the sum or product is even is 1. It will always happen.

1) Probability = 0 It will never happen
2) Probability to get a sum or product to be odd = 1 - (probability to get a sum AND product to be even). As Streetwolf mentioned, the only chance to get a sum and product even is that both dies show an even number. First die to get an even number is 3/6. For the second one, 3/6. Both dies to get even number = 3/6 * 3/6 = 1/4. BE CAREFULL!!! We are not done yet. We have to do one more calculation.

Probability to get a sum or product to be odd = 1 - (probability to get a sum AND product to be even = 1 - (1/4) = 3/4

So, the answer is 3/4.

c) answer = 1

correct me if I'm wrong

 

[Streetwolf]

Oops good catch. I must have forgotten what the question wanted after a couple calculations 😛

 

[DDSABeach]

Oops good catch. I must have forgotten what the question wanted after a couple calculations 😛

I am having a problem understanding all the different probablity problems. Which is more favorable?

1) Negation Rule - Calculates the probability of the occurrence of an event given the probability of its nonoccurence (or the reverse).
P(A) = 1 - P(nonA)

2) Basics of the Restricted Conjunction Rule - Calculates the probability of two (or more) events that happen independently of each other, such as flips of a coin or picking cards froma deck, when the first is returned before the second is drawn. P(A AND B) = P(A) X P(B)


3) The Restricted Disjunction Rule - Calculates the probability of the occurrence of one of two mutually exclusive events such as picking either an ace or a king.
P(A OR B) = P(A) + P(B)

4) The General Conjunction Rule -Calculates the probability of two (or more) events BOTH happening. When the events are independent of each other, P(B given A) = P (B) and this conjunction rule reduces to the restricted one.

P (A and B) + P (A) x P (B given A )

5) The General Disjunction Rule - Calculates the probability of the occurrence of one of two events. If the events are mutually exclusive, then P(A and B)=0 and the general disjunction rule reduces to the restricted one. Usually, A and B are picked to be independent of each other, Thus , P(A and B) = P(A) * P(B).
P(A or B) = P(A) + P(B) - P(A and B)

6) The basics of Simple Probability - n = the total number of observed cases
f = the number of cases favorable to the phenomenon whose probability is being calclated.
P(A) = f/n.

 

[Streetwolf]

Whichever is the easiest to come up with numbers for.

For #1 of his problem it was easiest to analyze the problem first and note that the two events never overlap. Thus the AND would make P = 0.

For #2 it was easier to come up with a probability for the AND part when you negate the statement.

For #3 it was easiest to negate #1 and come up with the probability.

 

[nanaschool2000]

I wish 100 precent of DAT is made up of MATH

I'm just whining. I'm getting really tired of memorizing all these organic reactions. Yesterday I watched this movie and it had a scene of a guy stabbing other person from the back. Then I thought of Nucleophillic Attack SN2 reaction. 🙁

 

[DDSABeach]

I wish 100 precent of DAT is made up of MATH

I'm just whining. I'm getting really tired of memorizing all these organic reactions. Yesterday I watched this movie and it had a scene of a guy stabbing other person from the back. Then I thought of Nucleophillic Attack SN2 reaction. 🙁

LOL, you got it bad!

 

[tRNA]

Thanks you all
no one has those answers for the kaplan lesson bk test??...plz post them if u do
thanks again

 

[Streetwolf]

Post the questions if you remember them. I'll give you the answers.