A coin has bias P(Heads) = 0.55. To simulate 12 coin tosses, what should xx not be in the following code?

set.seed(11)
rbinom(n = 12, 1, xx)

Question

A coin has bias P(Heads) = 0.55. To simulate 12 coin tosses, what should xx not be in the following code?

set.seed(11)
rbinom(n = 12, 1, xx)

BlackTom AI · Accepted Answer

The problem describes simulating 12 coin tosses using rbinom in R, with a biased coin where P(Heads) = 0.55. The code shown is set.seed(11); rbinom(n = 12, 1, xx). Here, the third argument of rbinom is the probability of success (p) for each Bernoulli trial.

First, I’ll restate what each part means: n = 12 means we want 12 independent trials, size = 1 indicates each trial yields a single Bernoulli outcome (0 or 1), and prob = xx is the probability of obtaining 1 (Heads) in each trial.

Next, evaluating potential values for xx: any value of xx in the interval [0, 1] defines a valid probability for Heads. If xx = 0, every toss yields 0 (Tails) deterministically; if xx = 1, every toss yields 1 (Heads) deterministically. Values strictly between 0 and 1 yield a genuine random biased outcome with the specified probability. Values outside the interval [0, 1] are invalid for the probability parameter and would typically produce an error.

Since the problem states the coin has bias P(Heads) = 0.55, the intended correct probability parameter should be xx = 0.55. Any other value within [0, 1] would simply specify a different bias and would not match the given 0.55 bias.

Regarding the prompt’s directive to identify what xx should not be: if the expectation is that xx should reflect the stated bias, then xx = 0.55 is the correct probability to model Heads, and a value outside [0, 1] would be inappropriate and invalid. The specific option provided in the answer field, heads=0.55, aligns with the intended bias specification; however, if the instruction is to identify a value that xx should not be, inappropriate candidates would include probabilities outside [0, 1] (e.g., 1.5 or -0.2) or a completely different interpretation such as treating Heads as 2 in a Bernoulli context, which would be invalid.

In summary, understanding the rbinom call clarifies that the probability parameter must be a valid probability in [0, 1]. For the stated bias of 0.55, xx should be set to 0.55 to accurately reflect P(Heads) = 0.55. Values that are not valid probabilities (outside [0, 1]) are not permissible for xx. If the question is asking for what xx should not be, the non-permissible choices are any numbers outside the [0, 1] range; among valid choices, 0.55 is the correct representation of the stated bias.

DATA1001/1901 (ND) Evaluate Quiz 6

A coin has bias P(Heads) = 0.55. To simulate 12 coin tosses, what should xx not be in the following code? set.seed(11) rbinom(n = 12, 1, xx)

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