Question

in each turn of a game you toss two coins. if 2 heads come up, you win 2 points and if 1 head comes up you win 1 point. if no heads come up, you lose 3 points. what is the expected value of the number of points for each turn? -0.25 0 0.25 0.5 complete this game is done favorable fair unfavorable

Explanation:

Step1: Calculate probabilities of outcomes

When tossing 2 coins, sample - space $S=\{HH, HT, TH, TT\}$, $n(S) = 4$.
$P(2\ heads)=\frac{1}{4}$, $P(1\ head)=\frac{2}{4}=\frac{1}{2}$, $P(0\ heads)=\frac{1}{4}$.

Step2: Determine points for each outcome

Let $X$ be the number of points. For 2 heads, $X = 2$; for 1 head, $X = 1$; for 0 heads, $X=-3$.

Step3: Calculate expected value

The formula for expected value $E(X)=\sum_{i}x_ip_i$.
$E(X)=2\times\frac{1}{4}+1\times\frac{1}{2}+(-3)\times\frac{1}{4}=\frac{2}{4}+\frac{1}{2}-\frac{3}{4}=\frac{2 + 2-3}{4}=\frac{1}{4}=0.25$.

Step4: Determine if the game is favorable

Since the expected value $E(X)=0.25>0$, the game is favorable.

Answer:

Expected value: 0.25
The game is: favorable