Unizor - Probability - Conditional - Problems 2

We recommend to attempt solving these problems prior to listening to the lecture or reading answers and proofs provided.
Also assume that all probabilities mentioned in the problems are not equal to zero, that is we are excluding impossible events.

Problem 2.1.
There are 3 white and 2 black socks in a box. You randomly pulled one sock and it happened to be white.
What is the probability of randomly pulling a second white sock?
Solve the problem in more than one way, try to use the concepts of conditional probability

Answer
1/2

Problem 2.2.
There is a computer game that has 2 levels. Experience shows that the probability of passing the level 1 during the first day equals to 50%=1/2. The probability of mastering both levels in the first day equals to 10%=1/10.
What is the probability of passing the level 2 during the first day for children who have managed to pass the level 1 on this day?

Answer
1/5

Problem 2.3.
There are three categories of people living in some place: 20% Jewish, 30% Muslims and 50% atheists.
The food restrictions among Jews and Muslims are similar, but not identical. Also, even among people of the same religion there are differences in interpretation of the laws.
Assume that 90% of Jewish people consider some food X as prohibited, while only 80% of Muslims agree with them. Atheists do not have any restrictions on food.
You invite a random person from a street for dinner. What is the probability that he would not eat the food X because he considers it prohibited?

Answer
0.42