Questions

A bag contains 6 red marbles and 4 yellow marbles. A marble is drawn at random and replaced. Two further draws are made, again without replacement. Find the probability of drawing:

1. three red marbles,
2. three yellow marbles,
3. no red marbles,
4. at least one red marble.

A six-sided dice is thrown three times. Draw a tree diagram, showing at each branch the two events: 'three' and 'not three' (written 3'). What is the probability of throwing a total of

1. three threes,
2. no threes,
3. one three,
4. at least one three?

A pot contains 4 red balls, 2 green balls, and 3 blue balls. A ball is drawn and not replaced. A second ball is drawn. Find the probability of drawing:

1. two blue balls
2. two red balls
3. one red ball and one blue ball (in any order).
4. one green ball and one red ball (in any order).

A bag contains 7 green discs and 3 blue discs. A disc is drawn and not replaced. A second disc is drawn. Draw a tree diagram. Find the probability that:

1. both discs are green
2. both discs are blue

A bag contains 5 red balls and 3 green balls. A ball is drawn and then replaced before another ball is drawn. Find the probability by using a tree diagram that:

1. two green balls are drawn.
2. the first ball is red and the second is green.

A bag contains 10 discs; 7 are black and 3 are white. A disc is selected and then replaced. A second disc is selected. Complete the tree diagram showing all the probabilities and outcomes. Find the probability of the following:

1. both discs are black.
2. both discs are white.

A box contains x milk chocolates and y plain chocolates. Two chocolates are selected at random Find, in terms of x and y, the probability of choosing:

1. a milk chocolate on the first choice
2. two milk chocolates 
3. one of each sort
4. two plain chocolates

There are 9 boys and 15 girls in a class. Three children are chosen at random. What is the probability that

1. all three are boys?
2. all three are girls?
3. one is a boy and two are girls. Give your answers as fractions.

A pot contains 3 red, 4 white, and 5 green balls. Two balls are selected without replacement. Find the probability that the three balls chosen are:

1. all red.
2. all green.
3. one of each colour.
4. If the selection of the two balls was carried out 1100 times, how often would you expect to choose two red balls?

The magnification is less than 1. What does it mean?