In a family of four children, what is the probability that there are at least two girls if the eldest child is a girl?
a)15/16 b)7/16 c)3/4 d)7/8 e)3/8
I'm not exactly sure how to even approach this problem; someone pretty please help me.
What is the probablity that the next three kids will be boys?
1/2*1/2*1/2
What is the probability of having at least one girl in next three? 1-prob next three is boys.
sorry, but I don't get it...
To solve this problem, we can use the concept of conditional probability. Conditional probability calculates the probability of an event happening given that another event has already occurred.
Let's break down the problem step by step:
Step 1: Understand the given information.
We know that there are four children in the family, and the eldest child is a girl. This means that we have already narrowed down the possibilities for the eldest child's gender - it must be a girl. So, we have one child out of four confirmed to be a girl.
Step 2: Determine the sample space.
The sample space represents all possible outcomes in the given scenario. Since we are considering the gender of four children, each child can be either a boy or a girl. So, the sample space consists of all possible combinations of genders for the four children. There are 2 possibilities (boy or girl) for each child, resulting in a total of 2^4 = 16 possible outcomes.
Step 3: Identify the favorable outcomes.
Now, we need to find the favorable outcomes where there are at least two girls among the four children, given that the eldest child is a girl.
Let's consider the possible genders for the three remaining children:
- 3 girls (GGGG)
- 2 girls and 1 boy (GGGB, GGBG, GBGG)
- 2 girls and 2 boys (GGGB, GGGB, GGBG, GBGG, BGGG)
- 1 girl and 2 boys (GBBG, GBGB, GGBB, BGBG, BGGB)
- 1 girl and 3 boys (GBGB, GGBB, BGBG, BGGB, BBGG)
- 4 boys (BBBB)
Out of these possibilities, three have at least two girls: 3 girls, 2 girls and 1 boy, and 2 girls and 2 boys. Therefore, there are three favorable outcomes.
Step 4: Calculate the probability.
Finally, we can calculate the probability using the formula: Probability = Favorable outcomes / Total outcomes.
In this case, the probability of having at least two girls, given that the eldest child is a girl, is: 3 (favorable outcomes) / 16 (total outcomes) = 3/16.
So, the answer is option b) 7/16.
I hope this explanation helps you understand how to approach and solve this problem.