To solve this problem, let's break down the details and the process of estimation.
First, consider the nature of the game. You have a 50% chance of winning [tex]$950 each time you play.
Since you're flipping a coin, the probability of either heads or tails occurring is 50%, or 0.5.
To estimate the expected value from playing this game, we'll use the formula for expected value:
\[ \text{Expected Value} = (\text{Probability of Win}) \times (\text{Win Amount}) \]
Here, the probability of winning (flipping heads or tails correctly) is 0.5, and the win amount is $[/tex]950.
Thus, the expected value:
[tex]\[ 0.5 \times 950 = 475 \][/tex]
Rounding to the nearest whole, this is closest to [tex]$500.
Therefore, by estimation, the best response would be:
$[/tex]500
