Conditional Probability and Venn Diagrams

In summary, the question is asking for the probability of both cars being Chevrolets, given that both are of the same make. The make refers to either a Jeep or a Chevrolet, and for each option, the probability is assigned as 1/2. However, the denominator should take into account that only 2 Chevrolets or 2 Jeeps can be selected, not a combination of both. Therefore, the probability would be 2/8 or C(8,2) for the number of ways to select 2 Chevrolets from the 8 available.
  • #1
navi
12
0
I am having a hard time with the following exercise:

Assume for this problem that the company has 8 Chevrolets and 4 Jeeps, and two cars are selected randomly and given to sales representatives.
What is the probability of both cars being Chevrolets, given that both are of the same make?

I have tried many different things, but I do not even understand the question. I am assuming make refers to either a Jeep or a Chevrolet, so for each I am assigning them a Pr of 1/2. The union of both cars being chevrolets and being of the same make should be 2/8? I think this because it is a Chevrolet, and among Chevrolets there are 8 and you can only pick out 2...? I am totally lost :(
 
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  • #2
navi said:
I am having a hard time with the following exercise:

Assume for this problem that the company has 8 Chevrolets and 4 Jeeps, and two cars are selected randomly and given to sales representatives.
What is the probability of both cars being Chevrolets, given that both are of the same make?

I have tried many different things, but I do not even understand the question. I am assuming make refers to either a Jeep or a Chevrolet, so for each I am assigning them a Pr of 1/2. The union of both cars being chevrolets and being of the same make should be 2/8? I think this because it is a Chevrolet, and among Chevrolets there are 8 and you can only pick out 2...? I am totally lost :(

Hi navi,

I agree this question is a little bite confusing. I interpret "given that both are the same make" as you can only show 2 Jeeps or 2 Chevrolet vehicles. You can't show 1 Jeep and 1 Chevrolet. This affects the denominator, where we divide by all possible outcomes.Let's focus on the Chevrolets. How many ways can we pick two 2 of them from the 8, assuming all of them are the same?
 
  • #3
Jameson said:
Hi navi,

I agree this question is a little bite confusing. I interpret "given that both are the same make" as you can only show 2 Jeeps or 2 Chevrolet vehicles. You can't show 1 Jeep and 1 Chevrolet. This affects the denominator, where we divide by all possible outcomes.Let's focus on the Chevrolets. How many ways can we pick two 2 of them from the 8, assuming all of them are the same?

Could it be C(8,2)?

(sorry, I am confused as to when I should use the combination formula and when I shouldnt)
 

FAQ: Conditional Probability and Venn Diagrams

What is conditional probability?

Conditional probability is the likelihood of an event occurring given that another event has already occurred. It is calculated by dividing the probability of the joint occurrence of both events by the probability of the first event.

How is conditional probability represented graphically?

Conditional probability can be represented using Venn diagrams. Venn diagrams are visual representations of sets and their relationships, with overlapping circles representing the intersection between different sets.

Can Venn diagrams be used to solve conditional probability problems?

Yes, Venn diagrams can be used to solve conditional probability problems by visually representing the given information and identifying the intersection between different sets. This allows for a better understanding of the relationships between events and can aid in calculating the conditional probability.

What is the formula for calculating conditional probability?

The formula for calculating conditional probability is P(A|B) = P(A and B) / P(B), where P(A|B) represents the conditional probability of event A given event B has occurred, P(A and B) represents the joint probability of both events occurring, and P(B) represents the probability of event B occurring.

How is conditional probability used in real life?

Conditional probability is used in many real-life scenarios, such as weather forecasting, medical diagnosis, and risk assessment. It can also be applied in decision-making, marketing strategies, and sports analytics, among others.

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