Question

25 POINTS!! Look over Chuck's work What is incorrect about the way Chuck interpreted his problem? What should have been a clue to Chuck that something was wrong?

Answer 1

Answer:

The mistake made by Chuck is misplacing the 17% as $P(A\cap B)$instead of $P(A|B)$.

Step-by-step explanation:

We can find the probability that a random student will be taking both Algebra 2 and Chemistry by using this Probability Formula:

$\boxed{ P(A|B)=\frac{P(A\cap B)}{P(B)} }$

However, before we can use the formula, we have to understand what is the meaning of each term.

Let:

• A = students who take Chemistry
• B = students who take Algebra 2

Then:

• $P(A|B)$ = probability of a student who is taking Algebra 2 will also be taking Chemistry
• $P(A\cap B)$ = probability of a student who takes Algebra 2 as well as Chemistry
• $P(B)$ = probability of a student who takes Algebra 2

Based on the data given by the question:

• $P(A|B)$ = 17% = 0.17
• $P(A\cap B)$ = which we have to find out
• $P(B)$ = 8% = 0.08

We can see the mistake made by Chuck is misplacing the 17% as $P(A\cap B)$instead of $P(A|B)$.

The correct way to find the probability is:

$\displaystyle P(A|B)=\frac{P(A\cap B)}{P(B)}$

$\displaystyle 0.17=\frac{P(A\cap B)}{0.08}$

$P(A\cap B)=0.17\times0.08$

$\bf P(A\cap B)=0.0136\ or\ 1.36\%$

Answer 2

Answer:

See below for explanation and corrections

Step-by-step explanation:

• The clue lies in the question itself, last sentence
  "What is the probability that a random student will be taking both Algebra 2 and Chemistry?"

• This implies joint probability P(A ∩ B). This joint probability is what is to be determined from the given information

The information given is

• Probability student takes Algebra 2 is 0.08 is correctly written as P(B) = 0.08
• However the second statement is interpreted wrong,
  The statement "The probability that a student who is taking Algebra 2 is taking Chemistry is 17%" is a conditional probability and should be P(B|A) Instead Chuck has interpreted this statement to be the joint probability P(A ∩ B) and given it a value of 0.17
  
• The following should rectify Chuck's work
  P(B) = 0.08
  P(B|A) = 0.17
  P(A ∩ B) = P(B ∩ A) = P(B|A) · P(A) = 0.17 * 0.08 = 0.0136 = 1.36%
  
• Corrected Probability P(A∩B) = 1.36%