Final answer:
To find the distribution of the number of tosses required to obtain the first tails when picking from 10 coins, 2 of which have tails on both sides, we can use the concept of geometric distribution to calculate the cumulative probabilities of getting tails on each toss.
Step-by-step explanation:
In this problem, we are asked to find the distribution of the number of tosses required to obtain the first tails when picking from 10 coins, 2 of which have tails on both sides.
To solve this problem, we need to consider the probabilities of getting tails on the different tosses and calculate the cumulative probability of getting tails for each toss. This can be done by using the concept of geometric distribution, which models the number of trials required to achieve the first success (getting tails in this case).
The probability of getting tails on the first toss is 2/10, as there are 2 coins with tails. The probability of getting tails on the second toss is (8/10)*(2/10), as there are 8 coins without tails and 2 coins with tails remaining. Similarly, for the third toss, the probability is (8/10)*(7/9)*(2/10), and so on.
We can calculate the cumulative probabilities for each toss and summarize the distribution of the number of tosses required to obtain the first tails.