Ian tossed a fistful of silver coins into the air, then picked up the 12 coins that landed heads up.Is this sample of the coins likely to be biased?yesnoSubmit

To determine if the sample of coins is likely to be biased, we can analyze the situation based on probability and expectations related to a fair coin toss.

Analysis

1. Understanding Coin Toss Probability: A fair coin has an equal chance of landing on heads or tails. This gives us a theoretical probability of: $P(\text{Heads}) = P(\text{Tails}) = 0.5$ For a set of $n$ fair coins, we would expect approximately half of them to land heads up.

2. Expected Number of Heads: If Ian tossed $n$ coins, the expected number of coins landing heads up would be: $\text{Expected heads} = n \times P(\text{Heads}) = n \times 0.5$ Hence, if Ian picked up 12 coins that landed heads up, it implies that the actual count deviates from the expected count, which raises questions about the randomness of the sample.

3. Considering Sample Size: If Ian tossed a small number of coins (for example, 12 coins), getting all heads is quite unlikely. However, if the number of coins tossed was significantly larger (say, 24 or more), picking up 12 heads can be plausible due to statistical variation, albeit still somewhat unlikely.

Conclusion

Based on our analysis, if only a small number of coins were tossed and a disproportionate number landed heads up, this indicates potential bias in the sampling method.

Thus, the sample of coins is likely to be biased.

Final Answer

Yes, the sample of coins is likely to be biased.