Statistics MCQ - Probabilities

11 An urn contains 5 red and 10 black balls. Eight of them are placed in another urn. The chance that the latter then contains 2 red and 6 black balls is

Number of ways in which 8 balls can be drawn
out of 15 is ¹⁵C₈
Number of ways of drawing 2 red balls is ⁵C₂
and corresponding to each of these ⁵C₂ ways
of drawing a red ball, there are ^IOC₅ ways of
drawing 6 black balls.
Hence total number of ways in which 2 red
and 6 black balls can be drawn = 5C₂ X 10C₆

Required Probability =

= 140/429

12 A has one share in a lottery in which there is 1 prize and 2 blanks; B has three shares in a lottery in which there are 3 prizes and 6 blanks; compare the probability of A's success to that of B's success is

A can draw a ticket in ³C₁= 3 ways.
Number of cases in which A can get a prize
is clearly 1.

Probability of A's success = 1/3

Again B can draw a ticket in Probability

Number of ways in which B gets all blanks

Probability

Number of ways of getting a prize
= 84 - 20 = 64

Thus, probability of B's success =

A's probability of success : B's probability
of success

Probability

13 If A and B are independent, then A and B' are also

P(A ∩ B') = P(A) - P(A ∩ B)

= P(A) - P(A) P(B)

= P(A) (1 - P(B)) = P(A) P(B')

Hence, A and B' are independent.

14 The chance that a leap year selected at random will contain 53 Sundays is

A leap year consists of 366 days, so that there
are 52 full weeks (and hence 52 Sundays) and
two extra days. These two days can be
(i) Monday, Tuesday
(ii) Tuesday, Wednesday,
(iii) Wednesday, Thursday
(iv) Thursday, Friday
(v) Friday, Saturday
(vi) Saturday, Sunday
(vii) Sunday, Monday
Of these 7 cases. the last two are favourable

Required probability = 2/7

15 P(A ∩ B'/C) + P(A ∩ B/C) = P(A/C)