Question

1. A sample space is S = {m, n, q, r, s}. Identify two events as U = {m, q, s} and V = {n, q, r} . The probabilities of some of the outcomes are given by the following table:

Outcome	m	n	q	r	s
Probability	0.18	0.16	?	0.24	0.21

a. Determine what P (q) must be.
b. Find P (U) .
c. Find P (V)

(2)  After creating the sample space for tossing three coins, please answer the following:
a. List the outcomes that correspond to the statement “All the coins are heads.”
b. List the outcomes that correspond to the statement “Not all the coins are heads.”
c. List the outcomes that correspond to the statement “All the coins are not heads.”

Answer 1

Q.1) Given that, a sample space S ={m,n,q,r,s}

U= { m, q ,s } ; V= { n, q , r}

P(m) = 0.18 , p(n) = 0.16 , p(r) = 0.24 , p(s) = 0.21

a) P( q ) = 1- { p(m) + p(n )+p(r)+p(s) }

P(q) = 0.21

b ) P( U ) = p(m)+p(q)+p(s) = 0.60

c) P(V)= p(n)+p(q)+p(r) =0.16+0.21+0.24 = 0.61

Q 2). When we toss three coins simultaneously, then the possible outcomes are,

S={ HHH,HHT,HTH,THH,HTT,THT,TTH,TTT}

Where H is denoted for head and T is denoted for Tail. Therefore the total number of outcomes are 2³ =8.

a) The outcomes corresponding to the statement "All the coins are Heads" is { HHH }.

b) The outcomes corresponding to the statement " Not All the coins are Heads" i.e. at most one coin show head .

The corresponding outcome is ,

{ HHT,HTH,THH,HTT,THT,TTH,TTT}

c) the outcome corresponding to the statement " All the coins are not heads " is { TTT }.