- #1

rock.freak667

Homework Helper

- 6,230

- 31

I did simplify the wording a bit.

## Homework Statement

a)Given 2 events, A & B, write in set notation

1)the event that at most A or B occurs

2) The event that exactly A or B occurs

## The Attempt at a Solution

n=intersect, u=union

1) P(AuB)=P(A)+P(B)-P(AuB)

2) Not sure

## Homework Statement

b)There are n people in a room, what is the probability that at least 2 have the same birthday?

## The Attempt at a Solution

P(no 2 having the same birthday)+P(at least 2 having the same birthday)=1

P(no 2 having the same birthday)=(365/365)*(364/365)

P(no 3 having the same birthday)=(365/365)*(364/365)*(363/365)

P(no 4 having the same birthday)=(365/365)*(364/365)*(363/365)*(362/365)

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P(no 'n' having the same birthday)=(365/365)*(364/365)*(363/365)*(362/365)*(361/365)*...*(365-n+1)/365)

It looks like the numerator should be 365! and the denominator, 365

^{n}, but I am not sure what happens to the 'n' in the numerator.

## Homework Statement

c)There's an offer of a choice of 4 designs, 3 different heating systems, a garage or carport, and a patio or screened porch. How many different plans aer available?

## The Attempt at a Solution

I think it would be 4*3*2*2 = 48

## Homework Statement

d)A fair coin is tossed until a head appears for the first time. The tosses are independent.

Give the sameple space and what is the probability that the first head appears when the toss number is odd.

## The Attempt at a Solution

S={H,TH,TTH,TTTH,TTTTH,TTTTTH,...}

Is that how it woud look?

For the odd numbered toss, it would be

P(H),P(TTH),P(TTTTH),...

= 1/2,1/8,1/32,1/128,...

which forms a GP with first term a=1/2 and common ratio r =1/4. So the sum to infinity is a/1-r

=(1/2)(1-0.25)=(1/2)*(4/3)=2/3