Math 1351 Fundamentals of Mathematics II (North Lake College) Midterm Formulas Ch. 9-12
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Probability (theoretical probability) of an event
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The likelihood that an event will happen. The number of ways that a given event can occur divided by the total number of outcomes from a sample space of equally likely outcomes. P( A) = n(A)/n(S)
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Experimental (empirical) probability
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An estimate of probability that the event happens, based on observed outcomes of repeated trials. The number times an event occurs divided by the total number of trials. P( event) = number of favorable outcomes/total number of possible outcomes
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Probability properties
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P(impossible event) =0 P(S) = 1, where S is the sample space For any event A, 0 = less than or equal to P(A) = greater than or equal to 1 If A and B are mutually exclusive events, then P(A union B) = P(A) + P(B) If A and B are any events then, P(A union B) = P(A) + P(B) - P(A intersection B) If A is any event and (A not happening) is the compliment, then P(A not happening) = 1- P(A)
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Mutually Exclusive events
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P(A or B) = P(A union B) = P(A) + P(B).
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Independent events
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P(Event 1 intersection Event 2) = P(Event 1) x P(Event 2).
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Conditional probability
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P(B given A) = P(A intersection B)/P(A).
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Odds
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Odds (favor) = number of favorable outcomes/number of unfavorable outcomes. Odds (against) = number of unfavorable outcomes/favorable outcomes.
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Expected Value
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A1 x P1 + A2 x P2 + A3 x P3 + ... An x Pn
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Factorial
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n! = n(n-1) x (n-2) x...3 x 2 x 1 0! = 1
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Permutations
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nPr = n! / (n-r) !
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Permutations of like objects
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n! / r1! x r2! x ... x rk!
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Combinations
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nCr = n! / r! (n - r) !
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Converting percents to degrees
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% in decimal form times 360
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Range
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The highest value - lowest value
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Mean
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Add all the values together then divide it by how many numbers there are
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Median (even numbers) within a set
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Place all the numbers in the set in order then cross off all the numbers till you reach the middle, but with a set with even numbers add the two numbers in the middle then divide by 2.
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Standard Deviation
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SD=√V=(√x-√(〖mean〗^2 ))+(√(x_2 )- √(〖mean〗^2 ))+⋯ / N (Note: square root everything)
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Varience
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SD=√V=(√x-√(〖mean〗^2 ))+(√(x_2 )- √(〖mean〗^2 ))+⋯ / N ( Final answer DO NOT square root)
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Interquartile
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Place all the numbers in order then cross them off till the median is found, then find the median of one half of the data so that is the lower quartile then repeat for the upper quartile, then take the upper quartile and subtract the lower quartile.
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Clock (minute hand)
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hand moves 360 degrees per 1 hour 6 degrees per 1 minute
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Conversion: hr to minute
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1 hr = 60 minutes
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Clock (hour hand)
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moves 360 degrees in 12 hours 0.05 degrees per 1 minute
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Conversion: degrees to minutes
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1 degree = 60 minutes
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Conversion: minutes to seconds
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1 minute = 60 seconds
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Circumference of a circle
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C = 2 (pi) (r)
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Diagonal of a polygon
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n (n-3) / 2
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Number of sides of a polygon given an interior angle
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( n-2) x 180 / n
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Paper reduction problem
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whole - whole (reduction) = desirable size
