The probability that Judith has meat for her evening meal is 0.2 and the probability she has fish is 0.35

The probability that Judith has meat for her evening meal is 0.2 and the probability she has fish is 0.35; otherwise she has a vegetarian dish. If she has meat, the probability that she has indigestion is 0.8, if she has fish the probability that she has indigestion is 0.5 and if she has a vegetarian dish the probability that she has indigestion is 0.1. Last night Judith had indigestion. Calculate the probability that she had meat for her evening meal.

Judith’s evening meal choices are characterized by specific probabilities: there is a 0.2 chance that she will have meat, a 0.35 chance that she will opt for fish, and the remaining probability, which is 0.45, indicates that she will choose a vegetarian dish. Each meal type is associated with a distinct probability of experiencing indigestion. Specifically, if Judith consumes meat, the likelihood of her suffering from indigestion rises to 0.8. In contrast, if she chooses fish, the probability of indigestion decreases to 0.5, while a vegetarian meal presents the lowest risk, with only a 0.1 probability of causing indigestion.

Given that Judith experienced indigestion last night, we can apply Bayes’ theorem to determine the probability that she had meat for her evening meal. To do this, we first need to calculate the total probability of indigestion occurring across all meal types. This involves multiplying the probability of each meal type by its corresponding probability of causing indigestion. Thus, the total probability of indigestion can be computed as follows: for meat, it is 0.2 multiplied by 0.8; for fish, it is 0.35 multiplied by 0.5; and for vegetarian, it is 0.45 multiplied by 0.1. Summing these values will yield the overall probability of indigestion.

Finally, to find the probability that Judith had meat given that she experienced indigestion, we will use the results from the previous calculations. According to Bayes’ theorem, this probability is calculated by taking the probability of having meat and experiencing indigestion, divided by the total probability of indigestion. This analysis is particularly relevant for students preparing for A Level Maths February Revision, as it illustrates the practical application of probability theory in real-life scenarios.