In Exercises 49-53, use counting principles to find the probability.
53. A corporation has six male senior executives and four female senior executives. Four senior executives are chosen at random to attend a technology seminar. What is the
probability of choosing
b. four women?

검증된 단계별 안내

Step 1: Understand the problem. We are tasked with finding the probability of selecting 4 women out of 4 chosen senior executives, given there are 6 male and 4 female senior executives in total. This is a problem involving combinations and probability.

Step 2: Calculate the total number of ways to choose 4 senior executives from the 10 available (6 males + 4 females). Use the combination formula: \( \binom{n}{r} = \frac{n!}{r!(n-r)!} \), where \( n \) is the total number of items and \( r \) is the number of items to choose.

Step 3: Calculate the number of ways to choose 4 women from the 4 available women. Again, use the combination formula \( \binom{n}{r} \). Here, \( n = 4 \) and \( r = 4 \).

Step 4: Compute the probability by dividing the number of favorable outcomes (choosing 4 women) by the total number of possible outcomes (choosing any 4 executives). The formula for probability is \( P = \frac{\text{favorable outcomes}}{\text{total outcomes}} \).

Step 5: Simplify the fraction obtained in Step 4 to express the probability in its simplest form.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Counting Principles

Counting principles, such as the fundamental counting principle, permutations, and combinations, are essential for determining the number of ways to select items from a set. In this context, combinations are particularly relevant as they allow us to calculate the number of ways to choose a specific number of executives from a larger group without regard to the order of selection.

Combinations

Combinations refer to the selection of items from a larger set where the order does not matter. The formula for combinations is given by C(n, k) = n! / (k!(n-k)!), where n is the total number of items, k is the number of items to choose, and '!' denotes factorial. This concept is crucial for calculating the number of ways to choose four women from the four available female executives.

Probability

Probability is a measure of the likelihood of an event occurring, expressed as a ratio of favorable outcomes to the total number of possible outcomes. In this scenario, the probability of selecting four women involves calculating the number of ways to choose four women and dividing it by the total number of ways to choose any four executives from the ten total executives.

In Exercises 49-53, use counting principles to find the probability.53. A corporation has six male senior executives and four female senior executives. Four senior executives are chosen at random to attend a technology seminar. What is theprobability of choosingb. four women?