Answered: In an experiment, college students…

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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In an experiment, college students were given either four quarters or a $1 bill and they could either keep the money or spend it on gum. The results are summarized in the table. Complete parts below.

	Purchased Gum	Kept the Money
Students Given Four Quarters	33	13
Students Given a $1 Bill	15	30

a. Find the probability of randomly selecting a student who spent the money, given that the student was given four quarters.

b. Find the probability of randomly selecting a student who kept the money, given that the student was given four quarters.

c. What do the preceding results suggest?choose below

A student given four quarters is more likely to have kept the money than a student given a $1 bill.

A student given four quarters is more likely to have kept the money.

A student given four quarters is more likely to have spent the money than a student given a $1 bill.

A student given four quarters is more likely to have spent the money.

Expert Solution

Step 1

Let A₁ and A₂ be the events such that the Students Given Four Quarters and Students Given a $1 Bill , respectively and B₁ and B₂ be the events such that the Students purchased gum and Students kept the money, respectively. Then, consider the table:

	B₁	B₂	P(A_i)
A₁	$\frac{33}{91}$	$\frac{13}{91}$	$\frac{33}{91} + \frac{13}{91} = \frac{46}{91}$
A₂	$\frac{15}{91}$	$\frac{30}{91}$	$\frac{15}{91} + \frac{30}{91} = \frac{45}{91}$
P(B_i)	$\frac{33}{91} + \frac{15}{91} = \frac{48}{91}$	$\frac{13}{91} + \frac{30}{91} = \frac{43}{91}$	1

a)Probability of randomly selecting a student who spent the money, given that the student was given four quarters=

$P (B_{1} | A_{1}) = \frac{P (B_{1} \cap A_{1})}{P (A_{1})} = \frac{\frac{33}{91}}{\frac{46}{91}} = \frac{33}{46}$

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