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Preguntas

United Kingdom
14 A bag contains a large number of beads of which \( 45 \% \) are yellow. A random sample of 20 beads is taken from the bag. Use the binomial distribution to find the probability that the sample contains: a fewer than 12 yellow beads ( 2 marks) ( 3 marks)
Probability Jan 22, 2025
13 A manufacturer produces large quantities of plastic chairs. It is known from previous records that \( 15 \% \) of these chairs are green. A random sample of 10 chairs is taken. a Define a suitable distribution to model the number of green chairs in this sample. ( 1 mark) b Find the probability of at least 5 green chairs in this sample. c Find the probability of exactly 2 green chairs in this sample. c marks) ( 3 marks)
Probability Jan 22, 2025
12 A six-sided die is biased. When the die is thrown the number 5 is twice as likely to appear as any other number. All the other faces are equally likely to appear. The die is thrown repeatedly. Find the probability that: a the first 5 will occur on the sixth throw b in the first eight throws there will be exactly three 5 s .
Probability Jan 22, 2025
12 A six-sided die is biased. When the die is thrown the number 5 is twice as likely to appear as any other number. All the other faces are equally likely to appear. The die is thrown repeatedly. Find the probability that: a the first 5 will occur on the sixth throw b in the first eight throws there will be exactly three 5 s .
Probability Jan 22, 2025
11 A computer game has three levels and one of the objectives of every level is to collect a diamond. The probability that Becca collects a diamond on the first level is \( \frac{4}{5} \), the second level is \( \frac{2}{3} \) and the third level is \( \frac{1}{2} \). The events are independent. a Draw a tree diagram to represent Becca collecting diamonds on the three levels of the game. ( 4 marks) Find the probability that Becca: i collects all three diamonds ii collects only one diamond. c Find the probability that she collects at least two diamonds each time she plays. ( 3 marks)
Probability Jan 22, 2025
Year 12 maths - week 17 applied homework 9 A survey of a group of students revealed that \( 85 \% \) have a mobile phone, \( 60 \% \) have an MP3 player and \( 5 \% \) have neither phone nor MP3 player. a Find the proportion of students who have both gadgets. b Draw a Venn diagram to represent this information. c A student is chosen at random. Find the probability that they only own a mobile phone. 3 marks) d Are the events 'own a mobile phone' and 'own an MP3 player' independent? Justify your answer.
Probability Jan 22, 2025
(c) Calculate \( \left(6.3 \times 10^{5}\right) \times\left(2.5 \times 10^{-2}\right) \) Give your answer in standard form.
Aritmética Jan 21, 2025
A large rock has a weight of \( 1.2 \times 10^{4} \) grams. Find, in standard form, the weight of 12 of these large rocks.
Aritmética Jan 21, 2025
The diameter of Neptune is \( 5.0 \times 10^{4} \mathrm{~km} \) The diameter of Mars is \( 6.8 \times 10^{3} \mathrm{~km} \) Calculate the difference between the diameter of Neptune and the diameter of Mars. Give your answer in standard form.
Aritmética Jan 21, 2025
21 One electron has a mass of \( 9.1 \times 10^{-31} \) grams. Find the mass of 250 of electrons.
Física Jan 21, 2025
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