You are here:
- Home
- Science
- Mathematics
- Advanced Math
- Binomial Probability
Advanced Math/Binomial Probability
Advertisement
Question
Assume that 13% of people are left-handed. If we select 5 people at random, find the probability of each outcome described below.
a) The first lefty is the fifth person chosen.
b) The are some lefties among the 5 people
c) The first lefty is the second or third person
d) There are exactly 3 lefties in the group.
e) There are at least 3 lefties in the group.
f) There are no more than 3 lefties in the group.
I appreciate your diligence and experience on the website. This is the only question that i can't seem to a consistent answer. It is by far harder than the other problems.
I wouldn't be surprised to see my professor asking you the answer to this and other questions. I doubt his experience and knowledge. Unfortunately I am paying the big-bucks to get little more than i already know.
Consider being a professor one day; you'd be great.
a) The first left is fifth means the first four were right handed.
The chance of being right handed is 1 - chance of being left handed.
That's 1 - 0.13 = 0.87. So the chances are (0.87)^4 * 0.13.
b) The chance of there being some lefties among 5 people is the same as 1 - chance of no lefties. The chance of being right handed, as was found in a, is 0.87, so take 0.87^5.
c) This says nothing about the other 4 people, so for the 2nd or third person to be a lefty, that's 0.13 + 0.13. Now we half to subtract off when they're both lefties, since that was counted twice.
0.26 - 0.13^2 = 0.26 - 0.0169 = 0.2431, so around a 23% chance.
d) There are exactly 3 lefties in the group of 5 people means we need to compute C(5,3) * 0.13^3 * 0.87^2. C(a,b) = a!/b!(b-a)!.
In this case, C(5,3) = 5!/3!2! = 120/12 = 10.
e) There are at least 3 lefties means that their could be 3, 4, or 5.
C(5,3) * 0.13^3 * 0.87^2 +
C(5,4) * 0.13^4 * 0.87^1 +
C(5,5) * 0.13^5.
The total comes out to under 0.02 just to check the answer.
C(5,3) = 10, C(5,4) = 5, C(5,5) = 1.
f) There are no more than 3 means there are not 4 or 5.
The line starting with C(5,4) * ... right above here is for 4.
The line starting C(5,5) * ... right above here is for 5.
Add those two together, then subtract the sum of them from 1.
Related Articles
Answers by Expert:
Scott A Wilson
Expertise
I can answer any question in general math, arithetic, discret math, algebra, box problems, geometry, filling a tank with water, trigonometry, pre-calculus, linear algebra, complex mathematics, probability, statistics, and most of anything else that relates to math. I can even tell you it takes me over 2,000 steps to go a mile, but is that relevant?
Experience
Experience in the area; I have tutored people in the above areas of mathematics for almost two years in AllExperts.com. I have tutored people here and there in mathematics since before I received a BS degree almost 25 years ago. In just two more years, I received an MS degree as well, but more on that later.
I tutored at OSU in the math center for all six years I was there. Most students offering assistance were juniors, seniors, or graduate students. I was allowed to tutor as a freshman.
I tutored at Mathnasium for well over a year.
I worked at The Boeing Company for over 5 years.
I received an MS degreee in Mathematics from Oregon State Univeristy.
The classes I took were over 100 hours of upper division credits in mathematical courses such as
calculus, statistics, probabilty, linear algrebra, powers, linear regression, matrices, and more.
I graduated with honors in both my BS and MS degrees.
Past/Present Clients: College Students at Oregon State University, various math people since college,
over 7,500 people on the PC from the US and rest the world.
Publications
My master's paper was published in the OSU journal.
The subject of it was Numerical Analysis used in shock waves and rarefaction fans.
It dealt with discontinuities that arose over time.
They were solved using the Leap Frog method.
That method was used and improvements of it were shown.
The improvements were by Enquist-Osher, Godunov, and Lax-Wendroff.
Education/Credentials
Master of Science at OSU with high honors in mathematics.
Bachelor of Science at OSU with high honors in mathematical sciences.
This degree involved mathematics, statistics, and computer science.
I also took sophmore level physics and chemistry while I was attending college.
On the side I took raquetball, but that's still not relevant.
Awards and Honors
I earned high honors in both my BS degree and MS degree from Oregon State.
I was in near the top in most of my classes. In several classes in mathematics, I was first.
In a class of over 100 students, I was always one of the first ones to complete the test.
I graduated with well over 50 credits in upper division mathematics.
Past/Present Clients
My clients have been students at OSU, people nearby, friends with math questions,
and several people every day on the PC, and you're probably make one more.
©2012 About.com, a part of The New York Times Company. All rights reserved.