We are given a table that partially represents the outcomes of tossing two unbiased coins. We need to complete the table and then calculate the probabilities of the following events: getting two heads, getting different outcomes, and getting at least one tail.

1. Problem Description

We are given a table that partially represents the outcomes of tossing two unbiased coins. We need to complete the table and then calculate the probabilities of the following events: getting two heads, getting different outcomes, and getting at least one tail.

2. Solution Steps

(a) Completing the outcome table:

The rows represent the outcome of Coin 2 and the columns represent the outcome of Coin

1. The entries in the table represent the combined outcomes.

| | Coin 1 (H) | Coin 1 (T) |

|--------|------------|------------|

| Coin 2 (H) | HH | HT |

| Coin 2 (T) | TH | TT |

(b) Calculating probabilities:

(i) Probability of getting two heads (HH):

There is one outcome (HH) out of four possible outcomes (HH, HT, TH, TT).

Therefore, the probability is $\frac{1}{4}$.

(ii) Probability of getting different outcomes:

The different outcomes are HT and TH. There are two such outcomes out of four possible outcomes.

Therefore, the probability is $\frac{2}{4} = \frac{1}{2}$.

(iii) Probability of getting at least one tail:

The outcomes with at least one tail are HT, TH, and TT. There are three such outcomes out of four possible outcomes.

Therefore, the probability is $\frac{3}{4}$.

3. Final Answer

(a) The completed table is:

| | Coin 1 (H) | Coin 1 (T) |

|--------|------------|------------|

| Coin 2 (H) | HH | HT |

| Coin 2 (T) | TH | TT |

(b) The probabilities are:

(i) Probability of getting two heads: $\frac{1}{4}$

(ii) Probability of getting different outcomes: $\frac{1}{2}$

(iii) Probability of getting at least one tail: $\frac{3}{4}$