## Probability Exercise: Marble Selection### Problem StatementSuppose a bag contains 12 marbles. Of these, 3 are orange and numbered from 1 to 3. The other 9 marbles are yellow and numbered from 1 to 9.### Questions#### (a) Probability of Orange or Number 2Suppose you pick one marble from the bag at random. Find the probability that the marble is orange or that it is numbered 2.- ○ 0.027- ○ 0.333- ○ 0.499- ○ 0.603#### (b) Two Orange MarblesSuppose you pick two marbles from the bag at random **without replacement**. Find the probability that both marbles are orange.- ○ 0.045- ○ 0.251- ○ 0.709- ○ 0.839#### (c) At Least One Orange MarbleSuppose you pick 4 marbles from the bag at random **with replacement**. Find the probability that you pick at least one orange marble.- ○ 0.436- ○ 0.527- ○ 0.684- ○ 0.707#### (d) Expected Value of Marble NumberSuppose you pick one marble from the bag at random. Find the expected value of its number.- ○ 0.287- ○ 0.797- ○ 4.25- ○ 7.443### Explanation of Concepts#### Calculating Probability- The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.#### With and Without Replacement- **With replacement** means each marble is returned to the bag before the next draw, maintaining the total number of marbles.- **Without replacement** means each marble is not returned, reducing the total number of marbles for subsequent draws.#### Expected Value- The expected value is a weighted average of all possible values, reflecting the average outcome if the experiment is repeated many times.

Suppose a bag contains 12 marbles. Of these, 3 are orange and are numbered from 1 to 3. The other 9 marbles are yellow and are numbered from 1 to 9. (a) Suppose you pick one marble from the bag at random. Find the probability that the marble is orange or that it is numbered 2. O 0.027 0.333 0.499 0.603 (b) Suppose you pick two marbles from the bag at random without replacement. Find the probability that both marbles are orange. 0.045 0.251 0.709 0.839 (c) Suppose you pick 4 marbles from the bag at random with replacement. Find the probability that you pick at least one orange marble. 0.436 0.527 0.684 0.707 (d) Suppose you pick one marble from the bag at random. Find the expected value of its number. 0.287 0.797 4.25 7.443

Suppose a bag contains 12 marbles. Of these, 3 are orange and are numbered from 1 to 3. The other 9 marbles are yellow and are numbered from 1 to 9. (a) Suppose you pick one marble from the bag at random. Find the probability that the marble is orange or that it is numbered 2. O 0.027 0.333 0.499 0.603 (b) Suppose you pick two marbles from the bag at random without replacement. Find the probability that both marbles are orange. 0.045 0.251 0.709 0.839 (c) Suppose you pick 4 marbles from the bag at random with replacement. Find the probability that you pick at least one orange marble. 0.436 0.527 0.684 0.707 (d) Suppose you pick one marble from the bag at random. Find the expected value of its number. 0.287 0.797 4.25 7.443

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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