6. In the Pirates of the Aegean video game, you may have to investigate 0, 1, 2, 3, 4, or 5grottoes without success before you finally locate a treasure chest. You conclude that theprobability you will have to investigate at most x grottoes without success is(x+1)5(x+1)and F(5) = 1. (Remember that n) = n(n-1)(n-2)...(n-k+1) is theF(X) = P(X ≤ x) = 1 -number of permutations (ordered lists without replacement) of k items from n possibilities.)a) What is the probability you will have to investigate exactly 3 grottoes without success?b) What is the expected number E(X) of grottoes you will investigate without success?c) What is the variance Var(X) of the number of grottoes you will investigate withoutsuccess?

a) probability that you will have to investigate exactly 3 grottoes without success = 0.1428 b)…

Answered: 6. In the Pirates of the Aegean video…

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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