A bag contains 9 red balls and 6 white balls. Suppose we choose 3 random balls. How many ways can we choose exactly 1 red ball?
in Statistics Answers by

Your answer

Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
To avoid this verification in future, please log in or register.

1 Answer

Imagine the balls are of two colours but of different sizes. This makes each red ball and white ball unique.

The possible colour outcomes are RRR, RRW, RWR, RWW, WRR, WRW, WWR, WWW.

But when we consider each ball as unique we get different numbers. For example, RRR could be R1R2R3, R1R2R4, R1R2R5, etc. The number of permutations is 9*8*7=504. The number of combinations is 504/6=84, because the number of ways of arranging 3 balls is 6. The permutation R1R2R3 is not the same as R2R3R1, for example. But the combination R1R2R3 is the same as the combination R2R3R1.

(1) The balls are picked at random and returned after selection.

Now consider probabilities. P(R) is the probability of picking a red ball, so P(R)=9/15=3/5 and 1-P(R)=P(W)=2/5. There are 3 ways of picking exactly one red: RWW, WRW, WWR and so P(RWW)=P(WRW)=P(WWR)=(3/5)(2/5)^2=12/125. Add the three together and we get 36/125. That means that if the number of outcomes is N, then the number of ways of picking just one red is 36N/125. So we need to define and find N. Considering the uniqueness of each ball there are 15^3=3375 outcomes. So N=3375 and 36/125 of 3375=972. There are 972 ways of selecting exactly one red ball (any one of 9 reds) out of a possible 3375 outcomes.

(2) The three balls are selected at the same time without returning any.

This alters the probability and the number of outcomes. N=2730 (=15*14*13). The probabilities also change. Let's look at RWW, WRW, WWR. P(RWW)=9/15*6/14*5/13; P(WRW)=6/15*9/14*5/13; P(WWR)=6/15*5/14*9/13. Note that these all have the same value=9/91, so when added together we have 27/91. When we apply this to N=2730, we get 27*2730/91=810 ways.

by Top Rated User (1.1m points)
reshown by

Lol. You hidden your own answer. cheeky

Yes, I realised there was another interpretation of the question.

I add you to ym favorites, so I know all your updates and activites you do on here.
Oh, that's how you do it!
Your the first Admin who ever talked to me!
And I may be the last!
NO! STOP BEING A  pessimist!
I've only had one Admin talk to me, a Super Admin.
What is a super admin?

I think they're part of the team that originally set up the site. But that's just a guess. There aren't many of them. Go to Users then the Special Users tab. There are 6 SA's. You can also see the Admins.

Give me da link.

Related questions

2 answers
asked Nov 8, 2011 in Statistics Answers by anonymous | 2.0k views
1 answer
asked Apr 14, 2014 in Other Math Topics by anonymous | 433 views
1 answer
asked Apr 27, 2017 in Statistics Answers by anonymous | 1.9k views
1 answer
Welcome to MathHomeworkAnswers.org, where students, teachers and math enthusiasts can ask and answer any math question. Get help and answers to any math problem including algebra, trigonometry, geometry, calculus, trigonometry, fractions, solving expression, simplifying expressions and more. Get answers to math questions. Help is always 100% free!

Most popular tags

algebra problems solving equations word problems calculating percentages math problem geometry problems calculus problems math fraction problems trigonometry problems rounding numbers simplifying expressions solve for x order of operations probability algebra pre algebra problems word problem evaluate the expression slope intercept form statistics problems factoring polynomials solving inequalities 6th grade math how to find y intercept equation of a line sequences and series algebra 2 problems logarithmic equations solving systems of equations by substitution dividing fractions greatest common factor square roots geometric shapes graphing linear equations long division solving systems of equations least to greatest dividing decimals substitution method proving trigonometric identities least common multiple factoring polynomials ratio and proportion trig identity precalculus problems standard form of an equation solving equations with fractions http: mathhomeworkanswers.org ask# function of x calculus slope of a line through 2 points algebraic expressions solving equations with variables on both sides college algebra domain of a function solving systems of equations by elimination differential equation algebra word problems distributive property solving quadratic equations perimeter of a rectangle trinomial factoring factors of a number fraction word problems slope of a line limit of a function greater than or less than geometry division fractions how to find x intercept differentiation exponents 8th grade math simplifying fractions geometry 10th grade equivalent fractions inverse function area of a triangle elimination method story problems standard deviation integral ratios simplify systems of equations containing three variables width of a rectangle percentages area of a circle circumference of a circle place value solving triangles parallel lines mathematical proofs solving linear equations 5th grade math mixed numbers to improper fractions scientific notation problems quadratic functions number of sides of a polygon length of a rectangle statistics zeros of a function prime factorization percents algebra 1 evaluating functions derivative of a function equation area of a rectangle lowest common denominator solving systems of equations by graphing integers algebra 2 diameter of a circle dividing polynomials vertex of a parabola calculus problem perpendicular lines combining like terms complex numbers geometry word problems converting fractions to decimals finding the nth term range of a function 4th grade math greatest to least ordered pairs functions radius of a circle least common denominator slope unit conversion solve for y calculators solving radical equations calculate distance between two points area word problems equation of a tangent line multiplying fractions chemistry binomial expansion place values absolute value round to the nearest tenth common denominator sets set builder notation please help me to answer this step by step significant figures simplifying radicals arithmetic sequences median age problem trigonometry graphing derivatives number patterns adding fractions radicals midpoint of a line roots of polynomials product of two consecutive numbers limits decimals compound interest please help pre-algebra problems divisibility rules graphing functions subtracting fractions angles numbers discrete mathematics volume of a cylinder simultaneous equations integration probability of an event comparing decimals factor by grouping vectors percentage expanded forms rational irrational numbers improper fractions to mixed numbers algebra1 matrices logarithms how to complete the square mean statistics problem analytic geometry geometry problem rounding decimals 5th grade math problems solving equations with variables solving quadratic equations by completing the square simplifying trigonometric equation using identities
87,441 questions
99,039 answers
2,422 comments
16,939 users