Question

a number cube is rolled and a coin is flipped.
how many possible outcomes are there?
what are the missing table values?
a =
<
b =
<

Explanation:

Step1: Find the number of possible outcomes

When rolling a cube (6 - sided) and flipping a coin (2 - sided), use the counting principle. The number of possible outcomes is the product of the number of outcomes of each event.
The number of outcomes when rolling a cube \(n_1 = 6\), and the number of outcomes when flipping a coin \(n_2=2\).
The total number of possible outcomes \(N=n_1\times n_2\).

$$N = 6\times2=12$$

Step2: Determine the values of \(a\) and \(b\)

For the coin - flip and cube - roll combinations:

• When the coin shows tails (T) and the cube shows 2, the coin - flip part for the combination should follow the pattern. Since for T1 and H1 (coin - flip: T and H, cube: 1), for T3 and H3 (coin - flip: T and H, cube: 3) etc., when the cube shows 2, if the coin shows tails, \(a = T2\)
• When the coin shows tails and the cube shows 6, following the pattern of T1 (cube = 1, coin = T), T2 (cube = 2, coin = T), …, T6 (but we already have T1 - T5 filled in a certain pattern. Looking at the structure of the table, when the cube shows 6 and following the coin - flip (tails) pattern, \(b=T6\)

Answer:

The number of possible outcomes is \(12\), \(a = T2\), \(b=T6\)