Mental Math The table shows the possible outcomes of spinning the given spinner and tossing a fair coin. Find the probability of spinning a 1 and tossing a head.

Question

1
2
3
4
5
H
1​,H
2​,H
3​,H
4​,H
5​,H
T
1​,T
2​,T
3​,T
4​,T
5​,T
1
2
3
4
5
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Part 1
The probability of spinning a 1 and tossing a head is
  
enter your response here.

Answer 1

To find the probability of spinning a 1 and tossing a head using the spinner and coin, we need to determine the total number of possible outcomes as well as the number of favorable outcomes.

Step 1: Count the possible outcomes

1. Spinner outcomes: The spinner has 5 sections (1, 2, 3, 4, 5).
2. Coin outcomes: The fair coin has 2 outcomes (Heads (H) or Tails (T)).

Thus, the total number of possible outcomes when spinning the spinner and tossing the coin is:

\[ \text{Total outcomes} = \text{Number of spinner outcomes} \times \text{Number of coin outcomes} = 5 \times 2 = 10 \]

Step 2: Count the favorable outcomes

The favorable outcome for this problem is spinning a 1 and tossing a head, which is represented as:

• \( 1, H \)

There is only 1 favorable outcome in this case.

Step 3: Calculate the probability

The probability \( P \) of an event is calculated using the formula:

\[ P(\text{event}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} \]

Substituting the values we have:

\[ P(\text{spinning a 1 and tossing a head}) = \frac{1}{10} \]

Final Answer

The probability of spinning a 1 and tossing a head is \(\frac{1}{10}\).