Question

5. Mia Rob each have three cards labeled 1,
2, and 3. They play a game based on the
following experiment. They each choose
one of their cards at random. Mia wins if
the sum of the numbers on the cards is less
than 4. Rob wins if the sum is greater than
4. The game is a tie if the sum is exactly 4.
a. What is the probability of the sum of the
cards being 4? (Hint: Draw a table to find
all the possible outcomes.)
b. Rob complains that the game is not fair
because it is not a fair experiment. Do
you agree or disagree? Why?

Answer 1

have you tried to draw a table?

Answer 2

no not yet. how should i draw it? 2 columns and 3rows?

Answer 3

I would make either 3 or 4 columns; first for the first card, second for the second card, third for the sum, and (maybe) fourth for the winner

Answer 4

like this? o.o

Answer 5

well, you have put the players names in the first column, so not quite.
don't worry about how many rows it has just yet, lets just make the columns like so

Answer 6

so imagine the first card drawn is a 1. Mark that on the table...what can the next card drawn be?

Answer 7

card 2? ..

Answer 8

I mean "what are the possible values of card 2?"
If I have drawn the card with the number 1 first, then the second card must have either the 2, or the 3, correct?

Answer 9

yeah.

Answer 10

but don't each of them have three cards labeled? so its 6 cards in total? .

Answer 11

ah good observation! I was not reading carefully enough. Let me change the name of the columns to avoid confusionso then if mia draws a 1, rob can have any of a 1, 2, or 3
write each possibility individually

Answer 12

better to start off with 1-1 for simplicity I guess