# bayes' theorem

1. ### The true proportion of respondents

Fellow, stats lovers! I am now trying to remember my early statistics course in order to solve the following problem: 1) During the survey, 40% of the population maintain interest in mathematics. 1000 people were interviewed. With what probability can it be argued that the proportion of...
2. ### Sensitivity of a diagnostic test

There is an exercise that I am not able to solve: Diagnostic tests A1 and A2 are used to detect the presence or absence of a disease. The results of A1 and A2 are a priori independent of the presence or absence of the disease. A1 and A2 have sensitivity Sen1 and Sen2, respectively. A new...
3. ### Bayes' formula question help

One percent of population cannot drive even if they try very very hard, but everyone applies for the driving license. The driving test fails those who cannot drive with a chance of 97%, but because the test has to be strict, it fails those who drive well with a probability of 3%. How likely it...
4. ### bayes's theorem and conditional probability question

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5. ### Bayes's Theorem

Hi! Say there is a deck of 100 cards: Red w/ numbers = 40 Red w/ figures=15 Black w/ numbers=35 Black w/ figures=10 The only information known is that 55% of the cards are red and 45% of the cards are black and 75% of the cards have numbers and 25% of the cards have figures. That is the...