Let's analyze the problem step by step.

Problem Breakdown:

You have four biased coins, A, B, C, and D. The probability that each coin will land on Heads is given as follows:

• Coin A: Probability = 0.33
• Coin B: Probability = 0.033
• Coin C: Probability = 1
• Coin D: Probability = 0.30

Part (a) - Which coin is most likely to land on Heads?

To determine which coin is most likely to land on Heads, you simply compare the given probabilities.

• Coin A: 0.33
• Coin B: 0.033
• Coin C: 1
• Coin D: 0.30

The highest probability is 1 (for Coin C). Therefore, Coin C is most likely to land on Heads.

Part (b) - Estimate the number of times coin B will land on Heads if thrown 2000 times.

To calculate the expected number of times Coin B will land on Heads, multiply the probability of getting Heads by the number of throws:

$\text{Expected number of Heads} = \text{Probability of Heads} \times \text{Number of Throws}$

For Coin B: $\text{Expected number of Heads} = 0.033 \times 2000 = 66$

So, Coin B is expected to land on Heads 66 times if thrown 2000 times.

Summary of Answers:

• (a) Coin C is most likely to land on Heads.
• (b) Coin B is expected to land on Heads 66 times out of 2000 throws.

Would you like further details or explanations on any part of this solution? Here are some related questions you might consider:

1. What would the expected outcome be if Coin A was thrown 1000 times?
2. How does changing the number of throws affect the expected number of Heads for any coin?
3. If Coin D is thrown 5000 times, how many times would it likely land on Heads?
4. What is the total expected number of Heads if all coins are thrown once?
5. How would the expected number of Heads for Coin B change if the probability was 0.05 instead?

Tip: Remember that in probability, multiplying the likelihood of an event by the number of trials gives you the expected outcome, which is useful for estimating real-world scenarios.