Two buckets are lying on a table. Bucket #1 has five red and two yellow balls in it. Bucket #2 contains three red and four yellow balls. In all of the questions below, the buckets start with this composition.Two balls are drawn at random from bucket #1. What is the probability that one is red and one is yellow?One ball is drawn at random from bucket #1 and placed into bucket #2. One ball is then drawn from bucket #2. What is the probability that this ball is red?Balls are drawn one by one from bucket #2 until a red ball is drawn. What is the probability that the first red ball is drawn on the third draw.

Answered: Two buckets are lying on a table.…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Two buckets are lying on a table. Bucket #1 has five red and two yellow balls in it. Bucket #2 contains three red and four yellow balls. In all of the questions below, the buckets start with this composition.
1. Two balls are drawn at random from bucket #1. What is the probability that one is red and one is yellow?
2. One ball is drawn at random from bucket #1 and placed into bucket #2. One ball is then drawn from bucket #2. What is the probability that this ball is red?
3. Balls are drawn one by one from bucket #2 until a red ball is drawn. What is the probability that the first red ball is drawn on the third draw.

Expert Solution

Step 1

Solution :

Given : Bucket 1: 5 red + 2 yellow = 7 balls

Bucket 2 : 3 red + 4 yellow = 7 balls

1) No. of ways 2 ball can be drawn from bucket 1 = $(\begin{matrix} 7 \\ 2 \end{matrix})$ = 21

Let, A: Getting one red ball and one yellow ball

$∴$ P ( A ) = $\frac{(\begin{matrix} 5 \\ 1 \end{matrix}) (\begin{matrix} 2 \\ 1 \end{matrix})}{(\begin{matrix} 7 \\ 2 \end{matrix})}$

= 0.4761

Answer : Probability of getting one red ball and one yellow ball from bucket 1 is 0.4761.

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