Permutations & Combinations
How many ways can you arrange the letters in “ABE”?
6 (3!)
What is the probability of drawing a green marble from a bag with 2 green and 4 white marbles?
2/6 or 1/3
Probability of drawing green marbles from each of two bags: Bag 1: 2G, 4W; Bag 2: 3G, 1W.
(2/6) × (3/4) = 1/2
Convert π/4 radians to degrees.
45°
What is the amplitude and period of y = 2sin(x)?
Amp = 2, Period = 2π
How many 4-digit arrangements can be made using the digits in 1984?
24 (4! because all digits are unique)
What is the probability of selecting a labeled ruler from 15 labeled and 10 unlabeled rulers?
15/25 = 3/5
P(ruler with labels first and without second) from 15 labeled and 10 unlabeled (no replacement)?
(15/25) × (10/24) = 1/4
Convert −620° to radians.
−31π/9
Find x-intercepts and max value of y = −3cos(x).
x-int = π/2, 3π/2; max = 0
How many different 7-character screen names can Abelardo make using “ABE” and digits from 1984?
6 × 24 = 144
amie will try out for basketball or baseball but not both. P(baseball and catcher) = 0.42. What’s P(basketball)?
0.58
P(yellow | large marble)? 7 LR, 5 LY, 3 SR, 5 SY
5/12 (5 yellow out of 12 large marbles)
If (4,1) is on the terminal side of angle Θ, what is sin(Θ)?
sin = 1/√17 = √17/17
Identify period and asymptotes of y = tan(x).
Period = π, Asymptotes at x = ±π/2, ±3π/2…
How many ways can a train be ordered if the locomotive is first and the caboose last with 7 cars in between?
7! = 5040
What is the probability that Teresa and Julia are both chosen randomly from 10 students?
1/45
How do you calculate conditional probability using frequency? (using P(A) and P(B))
P(A | B) = P(A ∩ B) / P(B)
Find all 6 trig functions if (4,1) is on terminal side.
sin = 1/√17, cos = 4/√17, tan = 1/4
csc = √17, sec = √17/4, cot = 4
Describe asymptotes of cotangent graph.
Asymptotes at multiples of π
From a group of 10, how many different 2-student combinations can be selected for a trip?
45 (10C2)
What’s the probability it will NOT rain in SF (80%) and Sydney (30%)?
(1 − 0.8)(1 − 0.3) = 0.2 × 0.7 = 0.14
What’s the general formula for independent compound probability? (using P(A) and P(B))
P(A and B) = P(A) × P(B)
Find the exact value of cos(2π/3) using the unit circle.
−1/2
Find the height of a building if angle of elevation = 9° and distance = 2000 ft.
height = 2000 × tan(9°) ≈ 316 ft