Statistics - Probabilities
- Option : A
- Explanation : 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 10C6Required Probability =
= 140/429
- Option : A
- Explanation : 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
Number of ways in which B gets all blanks
Number of ways of getting a prize
= 84 - 20 = 64Thus, probability of B's success =
A's probability of success : B's probability
of success
13. If A and B are independent, then A and B' are also
- Option : A
- Explanation : 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
- Option : B
- Explanation : 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 favourableRequired probability = 2/7
