# Question: Researchers are investigating the physical development of children over time

Researchers are investigating the physical development of children over time. In the study, children are given a physical aptitude test at several stages in their development. Let be the event that the child passes the physical aptitude test. Furthermore, let be the event that the child taking the test was a boy, and be the event that the child taking the test was a girl. The computer storing the data from this project experienced hard drive failure and only some of the data was recovered resulting in the partial database shown in the table. Use your knowledge of probability theory to fill in the missing items in the table.

## Answer to relevant Questions

An experiment consists of selecting two integers (n, k) such that 0 ≤ n < 5 and 0 ≤ n < 10. (a) How many outcomes are in the sample space? (b) What fraction of the outcomes in the sample space satisfy n > k? (c) What ...Suppose two events A and B are independent. (a) Is it true that A is independent of ? If yes, give a convincing proof, otherwise, give a counterexample. (b) Is it true that Ā is independent of ? If yes, give a ...In a certain lottery, six numbers are randomly chosen from the set {0, 1, 2… 49} (without replacement). To win the lottery, a player must guess correctly all six numbers but it is not necessary to specify in which order ...I deal myself 5 cards from a standard 52- card deck. Find the probabilities of each of the following events. (a) 2 of a kind, (b) 3 of a kind, (c) 2 pair (e. g., 2 eights and 2 queens), (d) A flush (5 cards all of the ...Show that the above formula for the probability of the union of two events can be generalized to three events as follows: Pr (A U B U C) = Pr (A) + Pr (B) + Pr(C) – Pr( A∩ B)– Pr( A∩ C)– Pr( B∩ C)+ Pr( A∩ B∩ ...Post your question