5. Mickey Mouse starts at the left upper-corner vertex and travels to the right lower-corner vertex of the following 8 x 8 grid. He can only walk to the neighboring rightvertex or to the vertex directly below his current position.(a) How many paths can Mickey follow on his journey? (Hint: Any sequence ofeight right or eight down moves will bring Mickey to his destination.)number of paths =(b) Suppose Minnie Mouse is at the circled vertex. What is the probability of theevent E that Mickey stops (by chance) at that vertex and visits Minnie on theway to his destination?P(E)(as a fraction in lowest terms);(as a numerical approximation)5

Answered: (a) How many paths can Mickey follow on…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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In a group of 80 students, there are 50 girls and 30 boys such that 65% of the girls graduated from private schools and 15% of the boys graduated from private schools. If a student is randomly selected from this group, find the probability that the selected student graduated from a private school (use the shown tree diagram for your solution). Private School girls Public School Private School boys Public School O 0.800 0.406 O 0.538 O 0.463
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Suppose we are interested in the pairwise intersection. What is the pairwise intersection for the following events? The set of possible outcomes are s = (1, 2, 3, 4, 5, 6) Suppose E = (1,3, 5); F = (4, 5,6); and G = (2,6) 3. Intersection event of F & G ANSWER
Kylie has 12 pieces of candy left in her Halloween bag. There are 8 pieces of chocolate and 4 pieces of non-chocolate. She chooses a piece of candy at random and then chooses another piece of candy, without replacement. Draw a tree diagram to represent this situation and use it to calculate the probabilities that she picks:Two pieces of chocolate No chocolate At least one piece of non-chocolate One piece of each type
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A conditional Probability: P(A | B) is asking what is the probability we get event A if we know that event B occurred. A useful formula: P (A | B) = ||| P(A and B) P(B) Or: P(A | B) = (remaining # of ways to get A) / (remaining number of possible outcomes) A bag has 5 red balls, 7 green balls, and 8 purple balls. Two balls are going to be selected. After the first ball is drawn it is NOT returned to the bag. Find the probability the second is a red ball if you know the first chosen is a red ball. If A = event a red ball is selected: P(A|A) = ?
Suppose that events A and B are mutually exclusive with P(A) = 1 2 and P(B) = 1 6 . (Enter your answers as fractions.) (a) Are A and B independent events? Explain how you know. Since the events are mutually exclusive we know P(A|B) = which P(A) and thus the events are . (b) Are A and B complementary events? Explain how you know. We know that P(A) + P(B) = . And, since P(A) + P(B) 1, the events A and B complementary events.
Philippus flips a fair coin 100 times. Let the outcome be the number of heads that he sees. Philippus now flip his fair coin n times. He is interested in the event "there are (strictly) more heads than tails." What's the probability of this event for the following values of n? (g) an arbitrary positive integer n

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