Final answer:
The probability that both men will get exactly two heads each is 0.375. The probability that one man will get no heads and the other man will get three heads is 0.015625.
Step-by-step explanation:
A) Probability that both men will get exactly two heads each:
Each man flips a coin three times. The total number of outcomes for each man is 23 = 8.
Out of these 8 outcomes, the number of outcomes where each man gets exactly two heads each is 3.
The probability is calculated by dividing the number of desired outcomes by the total number of possible outcomes:
P(A) = desired outcomes / total outcomes = 3 / 8 = 0.375
B) Probability that one man will get no heads and the other man will get three heads:
If one man gets no heads, then he gets all tails. The probability of getting all tails in three flips is 1/23 = 1/8. Similarly, the probability of getting all heads in three flips is also 1/23 = 1/8.
Since the events are independent, the probability of one man getting no heads and the other man getting three heads is the product of their individual probabilities:
P(B) = P(no heads) * P(three heads) = (1/8) * (1/8) = 1/64 = 0.015625