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MATH / Bag A contains 3 white and 2 red balls. Bag B contains 6 white and 3 red balls. One of the two bags will be chosen at random, and then two balls will be drawn from that bag at rand…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

Bag A contains 33 white and 22 red balls. Bag B contains 66 white and 33 red balls. One of the two bags will be chosen at random, and then two balls will be drawn from that bag at random without replacement. What is the probability that the two balls drawn will be the same color? Express your answer as a common fraction. [asy] size(140); defaultpen(linewidth(0.7)); pen darkness = linewidth(1.2); real r = 0.642; filldraw(circle((-0.931,2.701),r),gray(0.5)); filldraw(circle((1.534,2.633),r),white,darkness); filldraw(circle((0.356,2.842),r),white,darkness); filldraw(circle((1.026,2.385),r),gray(0.5)); filldraw(circle((-0.184,2.502),r),white,darkness); [/asy]
Plain-text mathematical notation (without MathML)
Bag A contains 3 white and 2 red balls. Bag B contains 6 white and 3 red balls. One of the two bags will be chosen at random, and then two balls will be drawn from that bag at random without replacement. What is the probability that the two balls drawn will be the same color? Express your answer as a common fraction. [asy] size(140); defaultpen(linewidth(0.7)); pen darkness = linewidth(1.2);
real r = 0.642;
filldraw(circle((-0.931,2.701),r),gray(0.5));

filldraw(circle((1.534,2.633),r),white,darkness);

filldraw(circle((0.356,2.842),r),white,darkness);

filldraw(circle((1.026,2.385),r),gray(0.5));

filldraw(circle((-0.184,2.502),r),white,darkness);

[/asy]
Original LaTeX notation
Bag A contains $3$ white and $2$ red balls. Bag B contains $6$ white and $3$ red balls. One of the two bags will be chosen at random, and then two balls will be drawn from that bag at random without replacement. What is the probability that the two balls drawn will be the same color? Express your answer as a common fraction. [asy] size(140); defaultpen(linewidth(0.7)); pen darkness = linewidth(1.2);
real r = 0.642;
filldraw(circle((-0.931,2.701),r),gray(0.5));

filldraw(circle((1.534,2.633),r),white,darkness);

filldraw(circle((0.356,2.842),r),white,darkness);

filldraw(circle((1.026,2.385),r),gray(0.5));

filldraw(circle((-0.184,2.502),r),white,darkness);

[/asy]

level

Level 4

type

Counting & Probability

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Source and history

task_id
8a4055ec-d871-5b75-8fef-8eb9ab477df8
task_key
counting~5fand~5fprobability--test--8a4055ec-d871-5b75-8fef-8eb9ab477df8
task_revision_id
1
config / split
counting_and_probability / test

Official source

initial import