(a) A bag contains 6 white shirts and 3 blue shirts. Three shirts are picked at random one after another with replacement. Determine the probability that:

1.  All three shirts are blue in colour, 
2.  Two shirts are white and one shirt is blue, 
3. One shirt is white and two shirts are blue.

In a yard there are 500 vehicles, of which 160 are cars, 130 are vans and the remaining are lorries. If every vehicle has an equal chance to leave, find the probability of:

(i)  A van leaving first,

(ii)  A lorry leaving first,

(iii)  A car leaving second if either a lorry or van had left first.

Two numbers are chosen at random from 1, 2 and 3. What is the probability that their sum is an odd number if repetition is not allowed?

If A and B are two events such that P(A) = ¹₄ , P(B) = ¹₂ and P , find P(A U B)?.

  If a number is to be chosen at random from the integers 1, 2, 3, ..., 11, 12. find the probability that:

(i)  It is an even number,

(ii)  It is divisible by 3.

(d) If in part 16(c) above, E₁ is the set of even numbers and E₂ the set of numbers that are divisible by 3, show whether E₁ and E₂ are mutually exclusive events.

Find the probability that a king appears in drawing single card from an Ordinary deck of 52 cards

A box contains 4 white balls and 5 black balls. Two balls are selected at random without replacement. Find the probability that

(i) Both are white balls

(ii) The first is black and the second is the white ball

A bag contains 6 white balls and 3 yellow balls. A ball is selected at random and not replaced.

Another ball is then selected. Find the probability of selecting one white ball and one yellow ball.

A die and a coin are tossed together. What is the probability of getting a tail and an even number?

A box contains 7 red balls and 14 black balls. Two balls are drawn at random without replacement.

(a) Draw a tree diagram to show the results of the drawing.

(b) Find the probability that both are black.

(c) Find the probability that they are of the same colour.

(d) Find the probability that the first is black and the second is red.

(e) Verify the probability rule P(A) + P(A?) = 1 by using the results in part (b).

The probability that Rose and Juma will be selected for A - level studies after completing their O- level studies are 0.4 and 0.7 respectively. Calculate the probability that:

1. both of them will be selected.
2. either Rose or Juma will be selected. (10 marks)

A farmer was given three seeds to germinate in a nursery. The probability that a seed will germinate is . Using a tree diagram, find the probability that at least two seeds will germinate.