The table provides data on Developed and Developing countries regarding whether their economies grew, declined, or remained stagnant over the period 2020 – 2023. Calculate various... The table provides data on Developed and Developing countries regarding whether their economies grew, declined, or remained stagnant over the period 2020 – 2023. Calculate various probabilities based on the provided data. Read more

Steps to Solve

1. Interpreting the Data

   From the table, we identify the total number of developed and developing countries:

   • Developed: 30
   • Developing: 5

   Total countries = $30 + 5 = 35$.

2. Calculating Developed Probability

   To find the probability that a randomly selected country is developed: $$ P(\text{Developed}) = \frac{\text{Number of Developed Countries}}{\text{Total Countries}} = \frac{30}{35} = 0.857 $$

3. Calculating Economy Growth Probability

   Next, we find the probability of the economy growing among all countries: $$ P(\text{Grew}) = \frac{\text{Total Grew}}{\text{Total Countries}} = \frac{30}{35} = 0.857 $$

4. Probability of Development Status

   To find the probability that a country is either developed or its economy grew: This involves considering both probabilities without overlap.

5. Application of Conditional Probability

   If we focus on a specific condition (developed and grew), then: $$ P(\text{Developed and Grew}) = P(\text{Grew} \mid \text{Developed}) = \frac{10}{30} = 0.333 $$

6. Understanding Mutual Exclusivity

   Events are mutually exclusive if they cannot occur at the same time. Since a country cannot both “grew” and “remained stagnant,” they are mutually exclusive.