Question

Two indistinguishable coins are tossed in such a way that it cannot be determined which coin is which. One coin has been weighted so that it comes up heads with probability 0.6 and tails with probability 0.4. The other coin is fair, and is equally likely to come up heads or tails.

(a) Give the sample space for the experiment of tossing the two coins at the same time. Your sample space should contain 3 outcomes.

Answer 1

The sample space for tossing two indistinguishable coins, one biased and one fair, consists of three outcomes: HH, TT, and HT/TH. HT and TH are considered the same outcome due to the indistinguishability of the coins.

Step-by-step explanation:

The concept discussed is related to probability and combinatorics within the field of mathematics. When two indistinguishable coins are tossed, one being biased and the other fair, the sample space consists of three outcomes instead of the usual four since we cannot distinguish between the coins. The outcomes of this experiment can be classified as two heads (HH), two tails (TT), or one head and one tail (HT/TH). Since the coins are indistinguishable, HT and TH count as the same outcome.

The probability of each outcome differs because one coin is biased. Calculating the probability of an outcome in this situation requires consideration of the individual probabilities for each coin. The fair coin has a probability of 0.5 for heads (H) or tails (T). The biased coin has a probability of 0.6 for heads and 0.4 for tails. To determine the likelihood of each outcome, we consider the combination of probabilities for each coin.