Answer:
a)
the probability that Fischer wins the match is 0.5714
b)
p( D = d ) = { [tex]( 0.3 )^{d-1[/tex] [tex](0.7)[/tex], d = 1, 2, 3, ........
[tex]0[/tex] otherwise
Step-by-step explanation:
Given that;
probability that Fischer wins the match, p = 4
probability that Spassky wins the match, q = 0.3
Match drawn, 1 - p - q = 1 - 0.4 - 0.3 = 0.7
(a) What is the probability that Fischer wins the match?
P( Fischer wins) = p/( p+q)
we substitute
P( Fischer wins) = 0.4 / ( 0.4 + 0.3)
P( Fischer wins) = 0.4 / 0.7
P( Fischer wins) = 0.5714
Therefore, the probability that Fischer wins the match is 0.5714
b) What is the PMF of the duration of the match?
let D represent the duration of the match
since the duration D of the match is a geometric random variable with parameter p + q,
the PMF will be;
p( D = d ) = [tex]( 1 - p - q )^{d-1[/tex] ( p + q )
= [tex]( 1 - 0.4 - 0.3 )^{d-1[/tex] ( 0.4 + 0.3 )
p( D = d ) = [tex]( 0.3 )^{d-1[/tex] ( 0.7)
that is, p( D = d ) = { [tex]( 0.3 )^{d-1[/tex] [tex](0.7)[/tex], d = 1, 2, 3, ........
[tex]0[/tex] otherwise
