The correct answer is #a=9/2#, but how could #a# be a fraction if George can only be awarded points as whole numbers?
George will play a game at the school fair in which he will toss a penny, a dime, and a quarter at the same time. He will receive 3 points for each coin that lands with heads face up. Let #a# represent the total number of points awarded on any toss of the coins. What is the expected value of #a# ?
George will play a game at the school fair in which he will toss a penny, a dime, and a quarter at the same time. He will receive 3 points for each coin that lands with heads face up. Let
2 Answers
Because the "expected value" is an average, not a count.
Explanation:
Let's look at all the possibilities with H being heads and T being tails.
This table exhausts every conceivable possibility, from tossing three heads, to tossing three tails.
Now, let's add up the points,
The expected value is just the average of the possible points, which is the sum of all the points, divided by the number of trials.
It's like asking, what is the average number of kids the typical American family has. The answer is often 2.5, even though people don't have 0.5 kids!
Explanation:
#"this question has to do with Probability (P)"#
#"the scale of probability is"#
#0<=P<=1#
#"where 0 is impossible and 1 is certain"#
#"if it was certain he obtained a head on each coin then"#
#rArra=(1xx3)+(1xx3)+(1xx3)=9" points"#
#"but the probability of a head "=1/2#
#rArra=(1/2xx3)+(1/2xx3)+(1/2xx3)#
#color(white)(rArra)=3/2+3/2+3/2#
#color(white)(rArra)=9/2#