<span>Probability = 0.063
Fourth try = 0.0973
Let X be the number of failed attempts at passing the test before the student passes. This
is a negative binomial or geometric variable with x â {0, 1, 2, 3, . . .}, p = P(success) = 0.7
and the number of successes to to observe r = 1. Thus the pmf is nb(x; 1, p) = (1 â’ p)
xp.
The probability P that the student passes on the third try means that there were x = 2
failed attempts or P = nb(2, ; 1, .7) = (.3)2
(.7) = 0.063 . The probability that the student
passes before the third try is that there were two or fewer failed attmpts, so P = P(X ≤
2) = nb(0, ; 1, .7) + nb(1, ; 1, .7) + nb(2, ; 1, .7) = (.3)0
(.7) + (.3)1
(.7) + (.3)2
(.7) = 0.973 .</span>
The formula is
A=p (1+rt)
A future value
P present value
R interest rate
T time in years
Rose investment
A=2,600×(1+0.041×9)
A=3,559.4
Dennis investment
A=2,200×(1+0.057×9)
A=3,328.6
So Rose investment is greater than Dennis investment by
3,559.4−3,328.6=230.8
Hope it helps!
Using the Pythagorean Theorem we can solve this:
20^2 + 6^2 = X^2
400 + 36 = x^2
436 = x^2
x = SQRT(436)
x = 20.9 feet long
