# Question: An experiment consists of tossing a coin twice and observing

An experiment consists of tossing a coin twice and observing the sequence of coin tosses. The sample space consists of four outcomes Î¾1 = (H, H), Î¾2 (H, T), Î¾3 (T, H), and Î¾4 (T, T). Suppose the coin is not evenly weighted such that we expect a heads to occur more often than tails and as a result, we assign the following probabilities to each of the four outcomes:

(a) Does this probability assignment satisfy the three axioms of probability?

(b) Given this probability assignment, what is Pr (first toss is head)?

(c) Given this probability assignment, what is Pr (Second toss is head)?

(a) Does this probability assignment satisfy the three axioms of probability?

(b) Given this probability assignment, what is Pr (first toss is head)?

(c) Given this probability assignment, what is Pr (Second toss is head)?

## Answer to relevant Questions

Repeat Exercise 2.12 if the probability assignment is changed to: An experiment consists of tossing a coin twice and observing the sequence of coin tosses. The sample space consists of four outcomes Î¾1 = (H, H), Î¾2 (H, ...Consider a modified version of the experiment where we flip a coin until the first occurrence of tails or until we flip the coin four times, whichever comes first. (a) List the possible outcomes of this experiment. How many ...Two balls are selected sequentially (without replacement) from an urn containing three red, four white, and five blue balls. (a) What is the probability that the first is red and the second blue? (b) What is the probability ...Prove the following identities involving the binomial coefficient An experiment consists of selecting a point from the interior of the unit circle, x2 + y2 1/2? (b) What fraction of the points in the space satisfies x2 + y2 > 1/2? (c) What fraction of the points in the space satisfy x + ...Post your question