Prompt Title: DDAI mid 1 paper

To calculate the probability using Bayes' theorem, we need to use the following formula:

$P(Play|Temp=Hot) = \frac{P(Temp=Hot|Play) \times P(Play)}{P(Temp=Hot)}$

Where:

• $P(Play|Temp=Hot)$ is the probability that the player can play given that the temperature is hot.
• $P(Temp=Hot|Play)$ is the probability that the temperature is hot given that the player can play.
• $P(Play)$ is the overall probability of playing.
• $P(Temp=Hot)$ is the overall probability of the temperature being hot.

Let's calculate each part:

1. Probability that the player can play ($P(Play)$)

We count the number of times the player plays and divide it by the total number of entries:

$P(Play) = \frac{\text{Number of 'Yes' in Play}}{\text{Total number of entries}}$

2. Probability that the temperature is hot given that the player can play ($P(Temp=Hot|Play)$)

We count the number of times the temperature is hot when the player plays and divide it by the total number of times the player plays:

$P(Temp=Hot|Play) = \frac{\text{Number of 'Hot' when 'Yes' in Play}}{\text{Number of 'Yes' in Play}}$

3. Probability that the temperature is hot ($P(Temp=Hot)$)

We count the number of times the temperature is hot and divide it by the total number of entries:

$P(Temp=Hot) = \frac{\text{Number of 'Hot'}}{\text{Total number of entries}}$

Let's calculate these probabilities:

• Number of 'Yes' in Play: 9
• Total number of entries: 14
• Number of 'Hot' when 'Yes' in Play: 4
• Number of 'Hot': 4

Now we can substitute these values into the formula to find $P(Play|Temp=Hot)$:

$P(Play|Temp=Hot) = \frac{\frac{4}{9} \times \frac{9}{14}}{\frac{4}{14}}$

$P(Play|Temp=Hot) = \frac{\frac{4}{9} \times \frac{9}{14}}{\frac{4}{14}}$

$P(Play|Temp=Hot) = \frac{\frac{4}{14}}{\frac{4}{14}} = 1$

So, given that the temperature is hot, the probability that the player can play is 1 or 100%.