Search & Filtering
There are 10 men and 10 women. Alice (woman) and Brad (man) never stand next to each other.
Assume that the men and women alternate in a line, how many possible ways are there for the
arrangement?
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
A chair is randomly selected.
(b) What is the probability that the chair that robot Q made is defective
(c) What is the probability of findings a broken chair
(d) Given that a chair is defective, what is the probability that it was not made by robot R
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)
Suppose A and B are mutually exclusive events defined on the same sample space such that P(A)=0.37 and P(B)=c.
1. What is the maximum value of c?
2. What is P(A|B)?
A company has 5 products in it’s Basics range, 5 products in it’s Standard range and 4 products in it’s Premium range. The company wishes to advertise in a local newspaper, but due to space constraints, it can only advertise 6 products.
- How many possible 6-product groupings/selections are possible?
- What is the probability that an advert of 6 randomly selected products contains an equal number of products from each of the ranges? (Round off to 1 decimal place.)
- What is the probability that an advert of 6 randomly selected products contains the whole Basics range and one item from the Standardrange? (Round off to 3 decimal places.)
- What is the probability that an advert of 6 randomly selected products contains the whole Basics range? (Round off to 3 decimal places.)
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?
A box contains 7 red, 3 green and 3 yellow balls. If two balls are drawn from the box, then what is the probability of getting
a) two red balls?
b) 1 red and 1 yellow balls?
c) non-red balls?
d) two green balls?
If a card is drawn from a deck of playing cards, then what is the probability of getting
a) a red card or a face card?
b) A diamond or a number below 6?
c) a black card or a spade?
The probabilities that a furnace station will supply melted products to 0,1,2,3,4, 5 or more temperature controlled trucks during a certain 30-minute period are 0.03, 0.18, 0.24, 0.28, 0.10 and 0.17. Find the probability that in this 30-minute period (a) more than two trucks received melted products (b) at most 4 trucks received melted products and (c) 4 or more trucks received melted products.
