Find the indicated probability. Round to four decimal places.
-Find the probability of at least 2 girls in 6 births. Assume that male and female births are equally likely and that the births are independent events.
A)0.6563
B)0.2344
C)0.8906
D)0.1094

Question

Find the indicated probability. Round to four decimal places.
-Find the probability of at least 2 girls in 6 births. Assume that male and female births are equally likely and that the births are independent events. 
A)0.6563
B)0.2344
C)0.8906
D)0.1094

Quizplus · Accepted Answer

The probability of at least 2 girls in 6 births can be found by subtracting the probability of getting 0 or 1 girl from 1. The probability of a girl in each birth is 0.5 (since male and female births are equally likely), and the events are independent. Using the binomial probability formula, P(X=k) = C(n, k) * p^k * (1-p)^(n-k), where C(n, k) is the combination of n items taken k at a time, p is the probability of success (having a girl in this case), n is the total number of trials (births), and k is the number of successful outcomes (girls). The probability of 0 girls is C(6, 0) * (0.5)^0 * (0.5)^6 = (1) * (1) * (0.015625) = 0.015625. The probability of 1 girl is C(6, 1) * (0.5)^1 * (0.5)^5 = (6) * (0.5) * (0.03125) = 0.09375. Adding these probabilities gives 0.015625 + 0.09375 = 0.109375. Subtracting this sum from 1 gives the probability of having at least 2 girls: 1 - 0.109375 = 0.890625, which rounds to 0.8906.

Find the Indicated Probability