List all possible outcomes when a six-sided die is rolled and a coin is flipped.
How many possible outcomes are there?
What are the missing table values?
a = ?
b = ?
Answer (2)
The total number of possible outcomes is the product of the die outcomes and coin outcomes: 6 × 2 = 12 .
'a' represents the outcome when the coin is heads and the die is 2, so a = H 2 .
'b' represents the outcome when the coin is tails and the die is 6, so b = T 6 .
The total number of outcomes is 12, a = H 2 , and b = T 6 , so the answers are 12 , H 2 , and T 6 .
Explanation
Understand the problem and provided data We are given a table representing all possible outcomes of rolling a six-sided die and flipping a coin. The table has rows for the coin flip (Heads or Tails) and columns for the die roll (1 to 6). We need to find the total number of possible outcomes and the missing values 'a' and 'b' in the table.
Calculate the total number of possible outcomes The total number of possible outcomes is the product of the number of outcomes for the die roll and the coin flip. The die has 6 possible outcomes (1, 2, 3, 4, 5, 6), and the coin has 2 possible outcomes (Heads, Tails). Therefore, the total number of possible outcomes is 6 × 2 = 12 .
Identify the value of 'a' The missing value 'a' represents the outcome when the coin shows heads (H) and the die shows 2. Following the pattern in the table, 'a' should be H 2.
Identify the value of 'b' The missing value 'b' represents the outcome when the coin shows tails (T) and the die shows 6. Following the pattern in the table, 'b' should be T 6.
State the final answer Therefore, there are 12 possible outcomes. The missing value 'a' is H 2, and the missing value 'b' is T 6.
Examples
This type of problem is useful in understanding basic probability. For example, if you wanted to know the probability of rolling a 3 and getting tails, you would look at the table and see that there is only one outcome (T 3) out of 12 possible outcomes. Therefore, the probability would be 12 1 .
There are a total of 12 possible outcomes when rolling a six-sided die and flipping a coin. The missing value 'a' is H 2 and the missing value 'b' is T 6. Thus, the total outcomes and missing values can be summarized clearly and accurately.
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