1.Calculate the probability of obtaining 2 heads in 2 tosses of a coin ,use tree diagram ,calculate the probability of obtaining a 2 followed by a 5 in 2 draws of a die use tree diagrams 

To solve the problems, we'll use tree diagrams and probability calculations. Let's break down each part:

### 1. Probability of Obtaining 2 Heads in 2 Tosses of a Coin

#### **Tree Diagram for Coin Tosses**

- **First Toss:** There are 2 possible outcomes: Head (H) or Tail (T).
- **Second Toss:** For each outcome of the first toss, there are again 2 possible outcomes: Head (H) or Tail (T).

The tree diagram would look like this:

```
       Start
        / \
      H     T
     / \   / \
    H   T H   T
```

#### **Outcomes and Probabilities**

- The possible outcomes from the tree diagram are: HH, HT, TH, TT.
- Each outcome has a probability of \(\frac{1}{2} \times \frac{1}{2} = \frac{1}{4}\).

To find the probability of getting 2 heads (HH):

\[
P(\text{HH}) = \frac{1}{4}
\]

### 2. Probability of Obtaining a 2 Followed by a 5 in 2 Draws of a Die

#### **Tree Diagram for Die Rolls**

- **First Roll:** There are 6 possible outcomes: 1, 2, 3, 4, 5, 6.
- **Second Roll:** For each outcome of the first roll, there are again 6 possible outcomes: 1, 2, 3, 4, 5, 6.

The tree diagram would look like this for the first few branches:

```
       Start
        / | \ ...
      1   2   3 ... 
     /|   /|  /|
    1 2  1 2 1 2 ...
```

#### **Outcomes and Probabilities**

- There are \(6 \times 6 = 36\) possible outcomes.
- The specific outcome of interest is rolling a 2 followed by a 5: (2, 5).

Each outcome has a probability of \(\frac{1}{6} \times \frac{1}{6} = \frac{1}{36}\).

Thus, the probability of rolling a 2 followed by a 5 is:

\[
P(2 \text{ followed by } 5) = \frac{1}{36}
\]

### Summary of Results:
1. **Probability of obtaining 2 heads in 2 tosses of a coin:** \(\frac{1}{4}\).
2. **Probability of obtaining a 2 followed by a 5 in 2 draws of a die:** \(\frac{1}{36}\).

Would you like more details on these calculations or explanations?

Here are some related questions to explore:

1. What is the probability of obtaining at least one head in 2 coin tosses?
2. How would the probability change if the coin was biased?
3. What is the probability of obtaining two 6s in 2 rolls of a die?
4. How would the tree diagram change if there were 3 tosses of a coin?
5. What is the probability of getting a tail followed by a head in 2 coin tosses?

**Tip:** Drawing tree diagrams is a great way to visualize and solve problems involving sequential events, especially when calculating probabilities.

Learn how to calculate the probability of obtaining 2 heads in 2 coin tosses and a 2 followed by a 5 in 2 die draws using tree diagrams and probability calculations. Understand the outcomes and probabilities for each scenario. Suitable for high school students learning about probability.

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