Step 1 :The problem provides a table that describes the probability distribution for the number of girls in 8 births. The random variable $x$ represents the number of girls.
Step 2 :Part (a) asks for the probability of getting exactly 6 girls in 8 births. From the table, we can see that the probability of getting exactly 6 girls is 0.117.
Step 3 :Part (b) asks for the probability of getting 6 or more girls in 8 births. This means we need to add up the probabilities of getting 6, 7, and 8 girls.
Step 4 :From the table, the probability of getting 6 girls is 0.117, the probability of getting 7 girls is 0.021, and the probability of getting 8 girls is 0.005.
Step 5 :Adding these probabilities together gives us a total probability of 0.143 for getting 6 or more girls in 8 births.
Step 6 :Final Answer: The probability of getting exactly 6 girls in 8 births is \(\boxed{0.117}\). The probability of getting 6 or more girls in 8 births is \(\boxed{0.143}\).