Probability questions | form four Basic Mathematics

Jeremia has two shirts, a white one and a blue one. He also has 3 trousers, a black, green and a
yellow one. What is the probability of Jeremia putting on a white shirt and a black trouser?

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.

If a number is to be chosen at random from the integers 1, 2, 3, . . . , 11, 12 ;

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.

A bag contains 6 red balls and 4 blue balls. A ball is. drawn£tlt random and then
replaced. Another ball is drawn. Use a tree diagram to find the probability that both
balls are blue .

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 Juma and Rose will be selected to join A-Level studies after completing their O-Level studies is 0.7 and 0.4 respectively.

Calculate the probability that

1. Both of them will be selected
2. Either Rose or Juma will be selected

The numbers 1 to 20 are each writen on a card, the 20 cards are then mixed together. One card is chosen at random from the pack.

Find the probabilty that the number on the card is

1. even
2. a factor of 24
3. prime

Box A has 10 light bulbs of which 4 are defective and box 13 has 6 light
bulbs of which 1 is defective, if a box is selected at random and then a bulb is
randomly drawn, calculate the probability that the bulb drawn is defective.