One hundred tickets are to be sold in a raffle. Two different tickets are to be drawn out for first and second prizes respectively.

A woman buys 8 tickets. Find the probability that:

i) she wins both prizes.

ii) she wins neither prize.

A box contains 4 good and 2 defective light bulbs. Two are drawn at random,

a) Complete the tree diagram.

b) What is the probability that the two light bulbs drawn are:

      (i) both defective;

      (ii) both good

      (iii) one defective and one good. 

A fair coin is tossed. If the result is heads, one marble is selected from a bag containing 3 red and 4 green marbles. If the result is tails, two marbles are selected from the same bag, without replacement.

Find the probability that at least one red marble will be selected.

One bag contains 2 red and 3 white marbles. Another bag contains 3 red and 4 white marbles. A bag is selected at random and two marbles are selected from the bag. What is the probability they are

i) Both red?

ii) Different colours?

Two hundred tickets are to be sold in a raffle. Two different tickets are to be drawn and are awarded first and second prize respectively. A man buys ten tickets. Find the probability that

i) He wins the first prize.
ii) He wins only the second prize.
iii) He wins both prizes.
iv) He wins neither prize.
v) He wins at least one prize.

A bag contains 8 red and 10 white marbles. Wayan randomly selects three marbles one at a time and without replacement. What is the probability that she selects \(\text{red, white, red}\)

i) in that order?

ii) in any order?

An urn contains five red, six blue and four yellow balls.Three balls are taken from the jar, without replacement. The probability of drawing one of each colour is?

In a drawer, there are 4 identical red socks and 4 identical blue socks. If two socks are selected at random, without replacement, then the probability that they do not match is? 

A bag contains 4 blue \((B)\) and 3 red \((R)\) balls. Two balls are drawn randomly from the bag. If the balls are not replaced after each drawing, then the probability of drawing two balls of the same colour is?

A bag contains 9 blue lollies and 7 green lollies.

Georgia takes out a lolly from the bag without looking and eats it. She then takes out another lolly without looking and eats it.

i) What is the probability of Georgia choosing a blue lolly in her first selection?

ii) By drawing a tree diagram, or otherwise, find the probability that Georgia eats two lollies of different colours.

A box contains 2 green (G) and 4 red (R) counters. Two counters are drawn randomly from the box. If the counters are not replaced after each drawing, then the probability of drawing 2 red counters is?

A jar contains 4 green (G),2 blue (B) and 4 red (R) marbles. Three marbles are drawn randomly from the jar. If the marbles are not replaced after each drawing, then the probability of not drawing 3 red marbles is?

A bag contains 5 green (G) and 4 red (R) balls. Two balls are drawn randomly from the bag. If the balls are not replaced after each drawing, then the probability of drawing 2 different coloured balls is?

A box contains 8 good and 4 defective batteries. Three are drawn at random, without replacement. The probability that three are defective is?

In a drawer there are six identical black socks and four identical green socks. If two socks are selected at random, without replacement, what is the probability that they are a matching pair?