Question

Sinead throws a fair dice and tosses an unbiased coin. What is the probability that she gets a six and a head? Choose one.

1/61/41/21/12

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Answer 1

Answer:

On the assumptions that (a) the die is an unbiased six-sided die (not weighted so that it favors one side more than another, (b) the coin is an unbiased two-sided coin (so that H and T are equally likely to occur), and (c) the coin flip and die roll are probabilistically independent of one another (so that the outcome of one does not affect the likelihood of the outcome of the other), the probability is 1/6 * 1/2, or 1/12.

If either the die or the coin (or both) is biased but the independence assumption still holds, the methodology is the same, but the resulting probability is different. E.g., suppose the die is weighted in favor of 6 so that a 6 comes up 1/4th of the time rather than 1/6th, and the coin is biased 60/40 in favor of heads, the probability you’re looking for is 1/4*(0.6), or 0.15.

If either the die or the coin (or both) is biased, but you don’t know the magnitude of the bias, or if the independence assumption doesn’t hold, then you’re SOL in terms of calculating the probability. You’d need more data.

Step-by-step explanation: