Question

In Exercises 29–32, use the given sample space or construct the required sample space to find the indicated probability.

Four Children Exercise 29 lists the sample space for a couple having three children. After identifying the sample space for a couple having four children, find the probability of getting three girls and one boy (in any order).

Accepted Answer

Step 1: Understand the problem. The couple has four children, and we need to identify the sample space for all possible gender combinations of these children. Each child can either be a boy (B) or a girl (G), so the sample space consists of all possible arrangements of B and G for four children. Step 2: Construct the sample space. Since there are four children, and each child has two possible outcomes (B or G), the total number of combinations is $$2^4 = 16. $$The sample space includes all permutations of B and G, such as {BBBB, BBGG, BGGB, etc.}. Write out all 16 combinations explicitly. Step 3: Identify the favorable outcomes. To find the probability of getting three girls and one boy, look for all arrangements in the sample space where there are exactly three G's and one B. For example, {GGGB, GGBG, GBGG, BGGG}. Count the number of such favorable outcomes. Step 4: Calculate the probability. The probability of an event is given by the formula P(Event) = (Number of favorable outcomes) / (Total number of outcomes in the sample space). Use the count of favorable outcomes from Step 3 and the total number of outcomes (16) to set up the probability calculation. Step 5: Simplify the probability expression. If needed, simplify the fraction obtained in Step 4 to its lowest terms to express the probability in its simplest form.

비슷한 문제에 대한 검증된 영상 답변:

주요 개념

Sample Space

Probability

Combinatorics