Probability Theory

We need to choose 6 economists to stay in the triple rooms, which can be done in:
ways.
After selecting 6 economists, we divide them into pairs for the 2 double rooms. The number of ways to divide 6 economists into pairs is:

Hence, the total number of ways is:

Thus, the correct answer is (a).

The only coins that can show heads are the first and third coins.
The third coin has a tail on the other side.
So, the probability is:

Thus, the correct answer is (b).

For a binomial distribution with parameters n (number of trials) and p (probability of success), the variance is given by:

Thus, the correct answer is (d).

When N (number of trials) is very large in a binomial distribution, it can be approximated by a normal distribution due to the Central Limit Theorem.

Hence, the correct answer is (c).

The probability of a head when one coin is tossed is the highest (50).
With more coins tossed, the probabilities of achieving exact numbers of heads decreases due to the binomial distribution.
Thus, the correct order is (A), (B), (C), (D).

Step 1: List all possible outcomes of two coin flips.
The possible outcomes are: 1. HH (Head, Head) 2. HT (Head, Tail) 3. TH (Tail, Head) 4. TT (Tail, Tail)

Step 2: Find the favorable outcomes.
The favorable outcomes are those with at least one head: HH, HT, and TH. Therefore, there are 3 favorable outcomes.

Step 3: Calculate the probability.
The probability is the ratio of favorable outcomes to total outcomes:

Step 4: Conclusion.
The probability of getting at least one head in two coin flips is .