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# PS-1

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.
Created by: deepak.bhavi