## Instructions

Homework 2 can be downloaded here on the ECE 302 course website.

## Problem 1: Unfair Coin Game

Bob, Carol, Ted and Alice take turns (in that order) tossing a coin with probability of tossing a Head, $P (H) = p$, where $0 < p < 1$. The first one to toss a Head wins the game. Calculate $P(B)$, $P(C)$, $P(T)$, and $P(A)$, the win probabilities for Bob, Carol, Ted and Alice, respectively. Also show that

• (a) $P (B) > P (C) > P (T ) > P (A)$
• (b) $P (B) + P (C) + P (T ) + P (A) = 1$

In how many ways can 8 people be seated in a row if

• (a) there are no restrictions on the seating arrangement;
• (b) persons $A$ and $B$ must sit next to each other;
• (c) there are 4 men and 4 women and no 2 men or 2 women can sit next to each other;
• (d) there are 5 men and they must sit next to each other;
• (e) there 4 married couples and each must sit together?

HW2.2 Brian Thomas_ECE302Fall2008sanghavi - On how to simplify the problem

HW2.2 Josh Long_ECE302Fall2008sanghavi - A's & Q's

## Problem 3: Trick Cards

Three identically shaped cards are put into a hat. One of the cards is red on both sides, another is blue on both sides, and the third card has one blue side and one red side. One card is pulled at random out of the hat, and one of its faces is randomly looked at. It turns out to be red. What is the probability the other face of the SAME card is ALSO red?

## Problem 4: Two-timer

A (foolish? courageous?) Purdue ECE undergrad had two girlfriends: one living south of campus and one living north of campus. To visit them, he decided it would be fair to randomly go to the bus stop, and take whichever bus (northbound or southbound) came first.

All he knew is that each northbound bus comes exactly 10 mins after the previous northbound bus, and each southbound exactly 10 mins after the previous southbound.

However, he found himself going to the northern girlfriend twice as often as the southern one. Why is this?

Hint: Think about the relative times of the buses.

HW2.4 Zhongtian Wang_ECE302Fall2008sanghavi- general procedure

## Problem 5: Redeye

SS booked a ticket on Priceline, and paid the price: he is flying from Indianapolis, through Seattle, to Chicago. At each place, there is a probability, $p$, of his bag being lost.

• (a) What is the probability his bag is lost? Hint: it is easier to find $P$(bag is NOT lost).
• (b) Given that his bag is lost, what is the conditional probability it is lost at each place?

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