Answer:
a. -$0.145
b. -$10
Step-by-step explanation:
Given:
Total Possible Throws = 372
Number of throws = 305
Let P(T) = Probability that the player makes the next throw
P(T) = 305/372
Probability that the player makes the next two throws is then given by:
Probability that he makes the next throw and he also makes the next throw.
= P(T) and P(T)
= P(T) * P(T)
= 305/372 * 305/372
= (305/372)²
= 0.672223667476008
= 0.672 -- Approximated
Let P(T') = Probability the the player doesn't make the next two throws
P(T') = 1 - P(T)
P(T') = 1 - 0.672
P(T') = 0.328
The expected gain for the player turns is given by:
(Probability of making both throws) * $5 + (Probability of NOT making both throws) x (-$10)
=0.627 * $5 + 0.328 * $10
= $3.135 - $3.28
= -$0.145
b.
Probability that he makes the next 626 throws
= P(T)^626
= (305/372)^626
= 1.027588097043E−54
Let P(T') = Probability the the player doesn't make the next two throws
P(T') = 1 - P(T)
P(T') = 1 - 1.027588097043E−54
P(T') = 1
The expected gain for the player turns is given by:
(Probability of making all 626 throws) * $5 + (Probability of NOT making all 626 throws) x (-$10)
=1.027588097043E−54 * $5 + 1 * -$10
= =1.027588097043E−54 * $5 - $10
= -$9.999999
= -$10
