Từ một hộp có 5 viên bi xanh và 7 viên bi đỏ với cùng kích thước và khối lượng. Lấy ngẫu nhiên 3 viên bi. Xác suất để 3 viên bi lấy ra có đủ 2 màu là
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Số cách lấy 3 viên bi từ 12 viên bi là $C_{12}^3 = \dfrac{12!}{3!9!} = \dfrac{12\times 11 \times 10}{3\times 2 \times 1} = 2 \times 11 \times 10 = 220$.
Số cách lấy 3 viên bi cùng màu là:
- 3 viên bi xanh: $C_5^3 = \dfrac{5!}{3!2!} = \dfrac{5\times 4}{2} = 10$
- 3 viên bi đỏ: $C_7^3 = \dfrac{7!}{3!4!} = \dfrac{7\times 6 \times 5}{3\times 2} = 7\times 5 = 35$
Số cách lấy 3 viên bi có đủ 2 màu là $220 - 45 = 175$.
Xác suất để 3 viên bi lấy ra có đủ 2 màu là $\dfrac{175}{220} = \dfrac{35}{44}$.
Câu hỏi liên quan
Trong các câu sau, có bao nhiêu câu là mệnh đề chứa biến?
a) Bạn học toán tốt không?
b) \(128\) chia hết cho \(4\).
c) \(5x-4>{{x}^{2}}\).
d) \(\left( 2n+3 \right)\) chia hết cho \(4\).
Cho hàm số \(y=f(x)\) có đạo hàm \(\forall x \in \mathbb{R}\), hàm số \(f^{\prime}(x)=x^{3}+a x^{2}+b x+c\) có đồ thị như hình vẽ.
Each of the following sentences has one error (A, B, C or D). Find it and blacken your choice on your answer sheet.
The key to the success of the project is the dedication of the team, all of which worked tirelessly to meet the deadline.
Phương án nào sau đây nêu đúng dạng nhị phân của số 57?
Theo em, chủ thể nào sau đây đang thực hiện hoạt động tiêu dùng?
- Dùng thông tin sau cho Câu 39 và Câu 40:
Hình bên biểu diễn sự thay đổi độ phóng xạ của một mẫu chất phóng xạ X theo thời gian.
Khối thị trường chung Nam Mỹ có tên viết tắt là gì?
Nếu hiệu điện thế giữa hai bản tụ tăng 4 lần thì điện dung của tụ
Cho hàm số y = f(x) có đồ thị như hình vẽ:
Khẳng định nào sau đây là đúng?
Read the following passage and mark the letter A, B, C, or D on your answer sheet to indicate the correct answer to each of the questions.
When parents name their children, they often take into consideration their own preferences, family traditions, or beliefs. In many European cultures, parents typically select names based on family connections, often honoring grandparents or ancestors. For instance, in Italy, children are commonly named after their grandparents, starting with the father's parents and then the mother's. Similarly, in Eastern Europe, children may be named after their deceased relatives to protect them from harm.
In some Asian countries, the naming process may involve the child's grandfather or a fortune-teller, who chooses a name believed to shape the child's character. Names might be inspired by elements like fire, water, earth, wood, or metal, or they may convey qualities such as beauty, strength, or kindness.
African cultures also have unique naming traditions, such as in Ghana's Akan culture, where a child's name is determined by the day of their birth. Each day has specific names for boys and girls, reflecting characteristics associated with that day. For example, a boy born on Friday might be named Kofi, symbolizing a "wanderer" or "explorer" while a girl born on the same day could be named Afua, also representing a traveler.
No matter where a name originates, it holds significant meaning and reflects the child's cultural heritage. Whether chosen out of preference or dictated by tradition, a child's name is a cherished and respected gift.
It can be inferred from the passage that names in China would relate to______.
Cho bảng số liệu:
GDP CỦA LIÊN BANG NGA QUA CÁC NĂM (Đơn vị: tỉ USD)
(Nguồn niên giám thống kê Việt Nam 2014, NXB Thống kê,2015)
Căn cứ vào bảng số liệu, cho biết nhận xét nào sau đây là chính xác về GDP của Liên bang Nga?
Cặp chất nào sau đây là đồng phân của nhau?
Read the following passage and mark the letter A, B, C, or D on your answer sheet to indicate the best answer to each of the following questions from 31 to 40.
Who are you?
On 6 June 2011, the media reported the kidnapping of a female Syrian-American blogger called Amina Arraf. Regarded as a daring political rebel, the 35-year-old had gained popularity for her blogs protesting the lack of freedom in Syria. Yet, only two days later, it was discovered that Amina had never existed. She was a fictional character created by Tom MacMaster, a forty-year-old American PhD student at the University of Edinburgh.
MacMaster's invention is an example of sock puppetry: the use of false identities to deceive others. (I). The false identity is known as a sock puppet, and its creator, a puppet master. (II). MacMaster created Amina to express his views on Middle Eastern affairs without offending other Americans. (III). Writing as Amina gave him the authority to say what he wanted. (IV).
At the turn of the millennium, Debbie Swenson created Kaycee Nicole, a fictional teenage girl suffering from terminal cancer. Her blog, Living Colours, described Kaycee’s struggle, attracting millions of readers. When Kaycee 'died' on 14 May 2001, her fans were devastated. Their distress turned to anger when they discovered that Kaycee was not real. Swenson had developed the character to gain attention and sympathy.
While Amina and Kaycee were used to meet their creators' needs, other identities have been invented for profit. American gun advocate John Lott made up a fake student, Mary Rosh, to defend his writing online and give him positive reviews. Mystery writer RJ Ellory fabricated a team of sock puppets to praise his own books and tear into those of his rivals. British historian Orlando Figes lost credibility when he had to publicly apologise for doing the same.
Yet none of these stories compare to large-scale sock puppetry today. The New York City Police Department has false identities on social media to catch criminals. The US military is believed to use sock puppets to track potential terrorists. It is clear that the internet is a minefield today and we all have to step very carefully in order not to get hurt.
According to the passage, which of the following statements is TRUE?
Read the following passage about the impact of social media on mental health and mark the letter A, B, C, or D on your answer sheet to indicate the best answer to each of the following questions
[I] In recent years, social media platforms have become a central part of daily life, offering users countless ways to connect, share, and communicate. [II] While these platforms offer many advantages, experts have noted rising concerns about their effects on mental health, particularly among young people (Smith & Anderson, 2018). [III] Studies reveal that excessive social media use can contribute to feelings of anxiety, depression, and loneliness, despite its intention to promote connection and social interaction (Twenge & Campbell, 2019). [IV]
A primary reason for these mental health concerns is the tendency for social media users to compare themselves to others. Platforms like Instagram and Facebook often highlight idealized lifestyles, leading users to feel inadequate about their own lives. Additionally, the constant notifications and messages contribute to a "fear of missing out," or FOMO, which keeps individuals in a cycle of checking their phones, often reducing the quality of sleep and overall well-being.
There is also a growing body of research suggesting a link between social media use and decreased attention spans. When users frequently switch between apps and notifications, their ability to focus for extended periods may diminish (Rosen, 2019). This shift in attention can interfere with productivity, especially in academic and professional settings, where sustained focus is essential.
Addressing these challenges requires a multi-faceted approach. Some mental health professionals suggest limiting screen time and setting boundaries, such as "device-free" hours before bedtime. Others recommend engaging in offline activities, like reading or exercising, to reduce dependence on social media and build healthier habits. According to psychologists, such strategies can bu mental resilience and allow for more meaningful, balanced relationships (Robinson & Smith, 2020).
Which of the following best summarizes the passage?
Read the following passage about The Key to a Fulfilling Life and mark the letter A, B, C or D on your answer sheet to indicate the option that best fits each of the numbered blanks from 18 to 22.
In today's fast-paced world, the importance of maintaining a healthy lifestyle cannot be overstated. (18)_________. For instance, those who engage in physical activities regularly often experience increased energy levels and improved mental well-being.
Moreover, research shows that (19)_________. Healthy habits, such as drinking plenty of water and getting enough sleep, contribute significantly to overall wellness.
(20)_________. It is essential to find activities that you genuinely enjoy, as this will make it easier to stay committed.
For example, many people find that yoga helps them manage stress while improving their flexibility. (21)_________. (22)_________.
In conclusion, making small changes to your daily routine can lead to significant improvements in your health and happiness. Embracing a healthy lifestyle is not just a trend; it’s a lifelong commitment to yourself.
Ngoài phần đất ở trung tâm Bắc Mĩ có diện tích hơn 8 triệu km2, Hoa Kì còn bao gồm bộ phận nào?
Trong một lớp học có 30 học sinh nam và 15 học sinh nữ. Muốn thành lập đội văn nghệ gồm 6 người, trong đó có ít nhất bốn nam. Hỏi có bao nhiêu cách?
Nội dung nào dưới đây không phản ánh đúng điều kiện tự nhiên của Hy Lạp và La Mã cổ đại?
Xác định ý đúng: Môi trường tự nhiên bao gồm các thành phần là gì ?
Mark the letter A, B, C, or D on your answer sheet to indicate the best arrangement of utterances or sentences to make a meaningful exchange or text in each of the following questions from 13 to 17
a. Engaging in hobbies and personal interests can have a profound impact on overall well-being.
b. These activities provide a much-needed break from the routine of daily life.
c. Dear Sam, I've been reflecting on our discussion about balancing work and personal life.
d. Hobbies also allow for personal growth and skill development.
e. Gardening, painting, or playing a musical instrument can foster creativity and boost self-esteem.