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PS-1
Question | Answer |
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When arranging 3 markers RBG, how are they independent events? | 1st marker can be chosen in 3 ways. Because of the reduction of markers, the choice for 2nd marker is down to 2.But we arent forced to pick G marker if 1st marker was R. Thus they are independent. |
What does the term 'Ask for independence' mean to you? | In order to apply the multiplication principle in a arrangement problem, the individual events must be independent of each other. |
What are the possible sums when a pair of dice is rolled? | The sums are distributed normally with a peak of 7, which occurs 6 times.2=1, 3=2...7=6, 8=5, 9=4...12=1 |
Probability of A and B P(A and B) = P(A) × P(B). What can you infer about P(A and B)? | A and B: the probability < than the individual probabilities of either A or B. This is because probability of any event is <=1. |
Probability of A or B, P(A or B) = P(A) + P(B). What can you infer about the P(A or B)? | A or B must occur: the probability > the individual probabilities of either A or B. This is an excellent strategy for eliminating certain answer choices |
If A and B are not independent, then the probability of A and B is P(A and B) = ? | P(A) × P(B|A)where P(B|A) is the conditional probability of B given A |
Concerning probability, give examples of independent and dependent events. | Separate drawings from a deck of cards are independent events if you put the cards back. An example of a dependent event, one in which the probability of the second event is affected by the first, is drawing a card from a deck but not returning it. |
What are the 3 methods to determine probability? | 1) Favorable outcomes/ All possible outcomes2) Via formulas: P(A and B), P(A or B). These are used when the events could be independent, dependent or mutually exclusive.3) Multiply individual probabilities of events |
What is P(A or B) if A and B are mutually exclusive? What if they are not mutually exclusive? | If exclusive, then P(A) + P(B). If not then P(A) + P(B) - P(A and B). |
What is the multiplication principle in counting methods? | Total no of outcomes of independent events=product of possible outcomes of each event individually |
What is POCNO? | Permutation Order Combination No Order |
What are the values of NPN and NCN respectively? | NPN=N!, NCN=1 |
In P&C, arrangement means? What do choosing/selection convey? | Arrangement=P, Selection/Choosing=C |
Sum and difference of two 2-digit numbers with interchanged digits are divisible? | Sum by 11; difference by 9 |
How do you express a 2 digit number pq? | 10p + q |
For same distance, if speed increases by 50%, time decreases by 33.33%? | Yes. For 25% increase, the decrease is 20%. Remember that these are increase/decrease percentages. So you will have to add/subtract from original figures to get new figures. |
Even/odd = ? | Even. Its same as mutiplying Even * 1/Odd; hence even. |
What are the units digits of 13^4,17^2, and 29^3? | 13^4 = 1 since 3*3*3*3=81.17^2 = 9 since 7*7=49. 29^3=9 since 9*9*9=729. Also units digit of 13^4*17^2*29^3=1 since 1*9*9=81 |
Formula for compound interest? | F = P (1 + r/n)^nt where F = Final amount, P= Principal, r=annual interest rate expressed as 0.08 for 8%,n=number of compounding periods per year,t=number of years |
In problems involving fractions, it is best to pick which numbers? | In problems involving fractions, it is best to pick numbers that are multiples of the denominators |
How to find the sum of a sequence of equally spaced numbers? | The solution can be found more efficiently by identifying the median of the set and multiplying by the number of terms |
What is the area of a trapezium? | The area of a trapezoid is equal to the product of the height times the average of the two bases |
If I think I can solve the problem by solving, should I? | Yes. With my fast calculations ability, I will be able to get the answer within 2 minutes. |
Should I be using the Plug-in technique more often? | Yes. I have not been employing it frequently enough. |
Only numbers ending in 3 or 7 yield a square ending in 9? | True |
What should you check when you calculate an answer that is not listed in the options? | Check if I have used the correct numbers from the problem. Very often, I misread a number thus calculating a wrong answer |
What concept should I think of in a problem of arithmetic mean (average)? | If average is given, think of the numbers in the set as + and - from the average. They should add up to zero. |