Three fair coins are tossed with possible outcomes of​ heads, H, and​ tails, T. Write a sample space with the equally likely outcomes. Then find the probability of tossing exactly 2 heads.

Question

Question content area bottom
Part 1
Complete the table
Sample Space
Toss 1
Toss 2
Toss 3
H
H
H
H
H
T
H
T
T
T
T
T
T
T
H
T
H
H
H
T
▼
T
H
T
H
▼
H
T

Answer 1

To create the sample space for tossing three fair coins, we will list all the possible combinations of heads (H) and tails (T). Each coin can either land on H or T, leading to the following outcomes:

1. HHH
2. HHT
3. HTH
4. HTT
5. THH
6. THT
7. TTH
8. TTT

Thus, the complete sample space is:

• HHH
• HHT
• HTH
• HTT
• THH
• THT
• TTH
• TTT

Part 1: Sample Space Table

Here is how we can organize the sample space into a table format:

| Toss 1 | Toss 2 | Toss 3 | |--------|--------|--------| | H | H | H | | H | H | T | | H | T | H | | H | T | T | | T | H | H | | T | H | T | | T | T | H | | T | T | T |

Part 2: Probability of tossing exactly 2 heads

Now, we need to find the probability of tossing exactly 2 heads. From the sample space, the outcomes that have exactly 2 heads (H) are:

1. HHT
2. HTH
3. THH

There are 3 outcomes that have exactly 2 heads.

The total number of outcomes in the sample space is 8 (as listed above).

Probability Calculation

The probability of getting exactly 2 heads is given by the formula:

\[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{3}{8} \]

Final Answer

Thus, the probability of tossing exactly 2 heads when three coins are tossed is \(\frac{3}{8}\).