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?

Answer 1

The expected value of the number of points for each turn is 0.25

What is expected value?

Expected value describes the long term average level of a random variable based on its probabilty distribution.

Now, Probability that 2 heads come up is

P(2 is H) = 1/4

Probability that 1 heads come up is

P(1 is H) = 2/4

⇒P(1 is H) = 1/2

Probability that no head will come up

P(no H's) = 1/4

Hence, the expected value for winning of 2points, 1point and  lose of3 points is given as-

Expected value = 2 * P(2 is H) + 1 * P(1 is H)  - 3 * P(no H's)

⇒Expected value = 2 * 1/4 + 1 * 1/2 - 3 * 1/4

= 0.5 + 0.5 - 0.75

⇒Expected value = 0.25

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