Question

Problem (11), 10 points 3 Math majors and 3 Computer Science majors will be presenting at a conference. Three students will be randomly selected to present on Monday, and the remaining three stu- dents will present on Tuesday.
(a, 3 points) What is the probability that two Computer Science majors and a math major will present on Tuesday? You do not need to simplify your answer.
(b, 5 points) Suppose we know at least one Math major has been selected to present on Monday. What is the probability that two Computer Science majors and a math major will present on Tuesday, given this information?
(c, 2 points) Based on your answer for b, are the events ‘at least one math major is selected to present on Monday' and 'two computer science majors and a math major present on Tuesday' independent?

Answer 1

Answer:

a}$P_1= 0.3$

b)$P_2 =0.45$

c) NOT INDEPENDENT

Step-by-step explanation:

From the question we are told that

Sample space

Math majors are 3

computer science majors are 3

Generally the sample space is

Mathematically the sample space required on Monday is given as  $S_m= 3c_1 * 3C_2$

where $S_m$ =sample space on Monday

Therefore,

$P_1$ = $\frac{3C_1 *3C_2}{6C_3}$

$P_1=\frac{3*3}{20}$

$P_1=\frac{6}{20}$

b)

Generally the the equation is given as

$P_2 =P(\frac{x \cap y}{y})$

where

x  is  selecting two math major and 1 computer science major on Monday

y is at leas one math major selected

$P_2 =\frac{^3C_1*^3C_2}{^3C_1*^3C_2 + ^3C_2*^3C_1 +^3C_3*^3C_0}$

$P_2 =\frac{3*3}{3*3 + 3*3 +^1*1}$

c)

Generally in representing independent events

$P_3=p(x \cap y)$

=>$p(x) * p(y)$

Mathematically

$n(x)= ^3C_1 *^3C_2$

$n(y)={^3C_1*^3C_2 + ^3C_2*^3C_1 +^3C_3*^3C_0}$

therefore

$n(x \cap y) =^3C_1 *^3C_2$

This does not satisfy the two equations stated above therefore NOT INDEPENDENT