Page 45 - Pra U STPM 2022 Penggal 3 - Maths (T)

Mathematics Semester 3 STPM Chapter 2 Probability
35. There are nine wrapping bags, three of which contain 2 GB pen drives and the rest 1 GB pen drives.
There are three girls and five boys randomly select a bag each. Find the probability that
(a) the girls select more bags which contain 2 GB pen drives than the boys,
(b) none of the girls has a bag which contain 2 GB pen drives.

36. The result of a diagnostic test for a certain infection may be negative or positive, but the test is not
completely reliable. If a person has the infection, the probability that the result will be negative is 0.02.
If a person does not have the infection, the probability that the result will be negative is 0.94. In a
certain population, the percentage affected by the infection is 7%.
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A person is chosen at random and tested.
(a) Find the probability that the result of the test is negative.
(b) If the result of the test is negative, show that the probability of the individual not infected is 2
0.9974, by giving your answer correct to four decimal places.

37. Ahmad and Suhaimi frequently play each other in a series of games of tennis. Records of the outcomes
of these games indicate that Ahmad has the probability 0.6 of winning the first game and that in every
subsequent game in the series, his probability of winning the game is 0.7 if he won the preceeding
game but only 0.5 if he lost the preceding game. A game cannot end in a draw. Find the probability
that Ahmad will win the third game in the next series he plays with Suhaimi.

38. A man goes to work by bus, taxi or MRT. The probability that he travels by MRT is 0.56 and he is
equally likely to take a bus or a taxi. The probability that he is late for work if he goes by bus, taxi or
MRT is 0.3, 0.2 or 0.1 respectively. Calculate the probability that
(a) he is late for work on a randomly chosen working day,
(b) he goes to work by bus if he is late for work,
(c) he is not late for work if he goes to work by bus or MRT.

39. A box contains 2 blue balls, 3 red balls and 4 green balls. Five balls are taken out at random from the
box without replacement. Calculate the probability that
(a) at least one ball is green,
(b) exactly three are red balls, given that at least one ball is green.

40. Let E and F be two events such that P(E) = 0.3, P(F) = 0.5, and P(E  F) = 0.7.

(a) Find P(E'  F' ).
(b) Determine whether the events E' and F' are
(i) mutually exclusive,
(ii) independent.

41. Two events, A and B, are such that P(A) = 0.4, P(B | A) = 0.5 and P(B | A' ) = 0.3.
(a) Find
(i) P(A  B)
(ii) P(A  B)
(iii) P(B)
(iv) P(A  B)
(b) Determine whether
(i) A and B are mutually exclusive. Explain.
(ii) A and B are independent. Explain.

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02 STPM Math(T) T3.indd 113 28/10/2021 10:21 AM