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In a workshop, three robots, Q, R and S, are employed to make chairs
Robot Q makes 25% of the chairs
Robot R makes 45% of the chairs
The remaining chairs are made by Robot S
Evidence has shown that 2 percent of the chairs made by robot Q are defective, 3 percent of the chairs made by robot R, and 5 percent of the chairs made by robot S are defective
(a) Construct a tree diagram that illustrates all possible outcomes and probabilities (5 marks)
In a workshop, three robots, Q, R and S, are employed to make chairs
Robot Q makes 25% of the chairs
Robot R makes 45% of the chairs
The remaining chairs are made by Robot S
Evidence has shown that 2 percent of the chairs made by robot Q are defective, 3 percent of the chairs made by robot R, and 5 percent of the chairs made by robot S are defective
(a) Construct a tree diagram that illustrates all possible outcomes and probabilities (5 marks)
An anonymous caller told the police that he saw a hit and run incident and had briefly seen the number plate of the car. He knew that the number plate started with two letters – a B and an E – but could not remember the order. After the letters were four digits – 3, 4, 8 and 9 – but again he could not remember the order. The four numbers were followed by the letter V. How many number plates will the police have to check to be sure of including the car involved in the hit and run incident?
When people visit a certain large shop, on average 34% of them do not buy anything, 53% spend less
than $50 and 13% spend at least $50.
(i) 15 people visiting the shop are chosen at random. Calculate the probability that at least 14 of
them buy something.
(ii) n people visiting the shop are chosen at random. The probability that none of them spends at
least $50 is less than 0.04. Find the smallest possible value of n.
Screws are sold in packets of 15. Faulty screws occur randomly. A large number of packets are tested
for faulty screws and the mean number of faulty screws per packet is found to be 1.2.
(i) Show that the variance of the number of faulty screws in a packet is 1.104.
(ii) Find the probability that a packet contains at most 2 faulty screws.
Damien buys 8 packets of screws at random.
(iii) Find the probability that there are exactly 7 packets in which there is at least 1 faulty screw.
Screws are sold in packets of 15. Faulty screws occur randomly. A large number of packets are tested for faulty screws and the mean number of faulty screws per packet is found to be 1.2. (i) Show that the variance of the number of faulty screws in a packet is 1.104
In a workshop, three robots, Q, R and S, are employed to make chairs
Robot Q makes 25% of the chairs
Robot R makes 45% of the chairs
The remaining chairs are made by Robot S
Evidence has shown that 2 percent of the chairs made by robot Q are defective, 3 percent of the chairs made by robot R, and 5 percent of the chairs made by robot S are defective
- Construct a tree diagram that illustrates all possible outcomes and probabilities
A chair is randomly selected.
- What is the probability that the chair that robot Q made is defective (1 marks)
(c) What is the probability of findings a broken chair (2 marks)
(d) Given that a chair is defective, what is the probability that it was not made by robot R (2 marks)
In a workshop, three robots, Q, R and S, are employed to make chairs
Robot Q makes 25% of the chairs
Robot R makes 45% of the chairs
The remaining chairs are made by Robot S
Evidence has shown that 2 percent of the chairs made by robot Q are defective, 3 percent of the chairs made by robot R, and 5 percent of the chairs made by robot S are defective
(a) Construct a tree diagram that illustrates all possible outcomes and probabilities (5 marks)
A chair is randomly selected.
(b) What is the probability that the chair that robot Q made is defective (1 marks)
(c) What is the probability of findings a broken chair (2 marks)
(d) Given that a chair is defective, what is the probability that it was not made by robot R (2 marks)
Suppose that a computer chip company has just shipped 10,000 computer chips to a computer company. Unfortunately, 20 of the chips are defective.
(a) Compute the probability that two randomly selected chips are defective using conditional probability.
(b) The probability that the first randomly selected chip is defective is 2010,000=0.002=0.2%. Compute the probability that two randomly selected chips are defective under the assumption of independent events.
6. Randomly a card is drawn from a deck of ordinary playing cards. You win LKR 1000 the card is a spade or an ace. What is the probability that you will win the game?
A. 1/13
B. 13/52
C. 4/13
D. 17/52
E. 18/52
