Question

he first date went well. You are still dating the same person and still looking for a great person to spend your life with. You are cautiously moving forward with the relationship and know that if they are a great match, their likelihood of being kind to animals is 0.9 whereas their likelihood of being kind to animals if they are not a great match is 0.7. You see that your prospective spouse is kind to animals. What is the probability that they are a great match now?

Answer 1

Answer:

0.125 = 12.5% probability that they are a great match now.

Step-by-step explanation:

To solve this question, we need the probability of a person being a great match, which i will use 0.1.

This question is solved using conditional probability.

Conditional Probability

We use the conditional probability formula to solve this question. It is

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

In which

P(B|A) is the probability of event B happening, given that A happened.

$P(A \cap B)$ is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Is kind to animals.

Event B: Is a great match.

Probability of being kind to animals:

0.9 of 0.1(Is a great match).

0.7 of 1 - 0.1 = 0.9(is not a great match). So

$P(A) = 0.9*0.1 + 0.7*0.9 = 0.72$

Probability of being kind to animals and a great match:

0.9 of 0.1. So

$P(A \cap B) = 0.9*0.1 = 0.09$

What is the probability that they are a great match now?

$P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.09}{0.72} = 0.125$

0.125 = 12.5% probability that they are a great match now.