Raymond B. answered • 06/11/22
Math, microeconomics or criminal justice
b 6 toonies 8 quarters in the bag. pick 3 randomly. what is the probability of getting 2 toonies and 1 quarter
(6/(6+8))^2(8/(6+8)
=(6/14)^2(8/14)
= (3/7)^2(4/7) = (3/7)(3/7)(4/7)
= (3)^2(4)/7^3
= 36/343
= about 11%
but multiply by 3 as there are 3 ways to get 2 toonies and 1 quarter: TTQ, TQT, QTT
11x3 = about 33% of 2 toonies and 1 quarter
or
there's 3 ways to get 2 toonies and 1 quarter
TTQ
TQT
QTT
TTQ has probability (6/14)(5/13)(8/12) = (3/7)(5/13)(2/3) = 30/273 = about 11%
P(TQT) = (6/14)(8/13)(5/12) = about 11%
P(QTT) = (8/14)(6/13)(5/12) = about 11%
multiply by 3 or add them up
90/273 = about 33%
or a little less than 33% chance
d 6 toonies and 24 quarters, pick 3 randomly what is the expected value?
4 times as many quarters as loonies, you expect 1/5 loonies and 4/5 quarters
or 3/5 loonie and 12/5 quarters
if you count the loonie as two dollars, the expected value = 6/5 + 48/5 = 54/5 = $10.80
but Canadian dollars are generally not equal to US dollars
1 CD = was about .783 US$ recently, although conversion rates constantly change. June 11, 2022, it's down to $0.78 US
a toonie= 2 CD = 2(.78) US dollars =about $1.56 per loonie
then
3/5(1.56) + 9.60 + .936 = about $10.54
so roughly $10.50 to $10.80 Maybe average it, $10.65 will be within 15 cents of the "correct" answer that the instructor or textbook is expecting, given how they intended the problem to read.
But odds are the problem expected you to tread a loonie = $2, so the answer they want is $10.80
or 10.8 dollars
C 6 loonies and 18 quarters Probability 3 coins will equal $2.50?
2 quarters = 50 cents. 1 loonie = $2
Probability of $2.50 is the same as the probability of getting 2 quarters and 1 loonie
3 ways to get 2 quarters and 1 loonie: QQL, QLQ, and LQQ
each has probability (18/24)^2(6/24) = (3/4)^2(1/4) = 9/64 = about .14.1
multiply by 3
P($2.50) = about 42%
or
(18/24)(17/23)(6/22) = (3/4)(17/23)(3/11) = 153/1012 = about 15%
multiply by 3
P(2.50) = about 45%
