Randall is playing a game that involves drawing a card from a deck. There are 10 cards numbered from 1 to 10. If Randall draws a card with a multiple of 3, he wins 5 points. If he draws any other card, he loses 3 points. What is Randall's expected point score when he draws a card?
3, 6 and 9 are multiples of 3. This means he has a 3/10 chance of getting +5 and 7/10 chance of a -3.
I hope this helps a little more. Thanks for asking.
To find Randall's expected point score when he draws a card, we need to calculate the expected value. The expected value is the average value that Randall can expect to get over the long run.
To calculate this, we need to consider the probabilities of drawing each card and the corresponding point values.
There are 10 cards in total, numbered from 1 to 10. Out of these, there are 3 cards that are multiples of 3, namely 3, 6, and 9. The remaining 7 cards are not multiples of 3.
The probability of drawing a multiple of 3 is given by: Probability(multiple of 3) = Number of multiples of 3 / Total number of cards = 3 / 10
Similarly, the probability of drawing a card that is not a multiple of 3 is: Probability(not multiple of 3) = Number of cards not multiples of 3 / Total number of cards = 7 / 10
Now, we can calculate the expected point score:
Expected score = (Probability(multiple of 3) * Point value for multiple of 3) + (Probability(not multiple of 3) * Point value for not multiple of 3)
Using the given information:
Point value for multiple of 3 = 5 points
Point value for not multiple of 3 = -3 points
Expected score = (3/10 * 5) + (7/10 * -3)
Expected score = 15/10 - 21/10
Expected score = -6/10
Expected score = -0.6
So, Randall's expected point score when he draws a card is -0.6 points.