To compute the odds in favor of obtaining exactly two tails when a coin is tossed three times, we can follow these steps:

Step 1: List all possible outcomes

When a coin is tossed 3 times, each toss has two possible outcomes: heads (H) or tails (T). The total number of possible outcomes is:

$2^3 = 8$

These outcomes are:

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

Step 2: Count the favorable outcomes

We are interested in the outcomes where there are exactly two tails. These are:

• HTT
• THT
• TTH

There are 3 favorable outcomes.

Step 3: Count the unfavorable outcomes

The remaining outcomes that do not have exactly two tails are:

• HHH
• HHT
• HTH
• TTT

There are 4 unfavorable outcomes.

Step 4: Compute the odds in favor

The odds in favor of an event are given by the ratio of favorable outcomes to unfavorable outcomes:

$\text{Odds in favor} = \frac{\text{Number of favorable outcomes}}{\text{Number of unfavorable outcomes}} = \frac{3}{4}$

So, the odds in favor of obtaining exactly two tails are 3:4.

Would you like more details or have any questions?

Here are five related questions you might find interesting:

1. What are the odds against obtaining exactly two tails when a coin is tossed 3 times?
2. How many tails can you expect on average when tossing a coin 3 times?
3. What is the probability of getting at least one tail when a coin is tossed 3 times?
4. How does the probability of getting two tails change if the coin is biased towards heads?
5. What is the probability of getting exactly one head when tossing a coin 3 times?

Tip: When calculating odds, always remember they compare favorable outcomes to unfavorable outcomes, whereas probabilities compare favorable outcomes to the total number of possible outcomes.