Advertisements
Advertisements
प्रश्न
Two dice are thrown. The events A, B, C, D, E and F are described as:
A = Getting an even number on the first die.
B = Getting an odd number on the first die.
C = Getting at most 5 as sum of the numbers on the two dice.
D = Getting the sum of the numbers on the dice greater than 5 but less than 10.
E = Getting at least 10 as the sum of the numbers on the dice.
F = Getting an odd number on one of the dice.
State true or false:
- A and B are mutually exclusive.
- A and B are mutually exclusive and exhaustive events.
- A and C are mutually exclusive events.
- C and D are mutually exclusive and exhaustive events.
- C, D and E are mutually exclusive and exhaustive events.
- A' and B' are mutually exclusive events.
- A, B, F are mutually exclusive and exhaustive events.
उत्तर
When two dices are thrown, there are 62 = 36 possible outcomes.
A = Getting an even number on the first dice
= {(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (4, 1), (4, 2), (4, 3), (4,4), (4, 5), (4, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}
B = Getting an odd number on the first dice
= {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6) }
C = Getting at most 5 as the sum of the numbers on the two dices.
= {(1, 1), (1, 2), (1, 3), (1, 4), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (4, 1)}
D = Getting a sum greater than 5 but less than 10
= {(1, 5), (1, 6), (2, 4), (2, 5), (2, 6), (3, 3), (3, 4), (3, 5), (3, 6), (4, 2), (4, 3), (4, 4), (4, 5), (5, 1), (5, 2), (5, 3), (5, 4), (6, 1), (6, 2), (6, 3)}
E = Getting at least 10 as the sum of the numbers on the dices
= {(4, 6), (5, 5), (5, 6), (6, 4), (6, 5), (6, 6)}
F = Getting an odd number on one of the dices
= {(1, 2), (1, 4), (1, 6), (2, 1), (2, 3), (2, 5), (3, 2), (3, 4), (3, 6), (4, 1), (4, 3), (4, 5), (5, 2), (5, 4), (5, 6), (6, 1), (6, 3), (6, 5)}
Now,
- True, because A ∩ B = Φ
- True, because A ∩ B = Φ and A ∪ B = S
- False, because A ∩ C ≠ Φ
- False, because C ∩ D = Φ but C ∪ D ≠ S
- True, because C ∩ D ∩ E = Φ and C ∪ D ∪ E = S
- True, because A' ∩ B' = Φ
- False, because A ∩ B ∩ F ≠ Φ and A ∪ B ∪ F = S
APPEARS IN
संबंधित प्रश्न
An experiment involves rolling a pair of dice and recording the numbers that come up. Describe the following events:
A: the sum is greater than 8, B: 2 occurs on either die
C: The sum is at least 7 and a multiple of 3.
Which pairs of these events are mutually exclusive?
Three coins are tossed. Describe two events which are mutually exclusive.
Three coins are tossed. Describe two events, which are not mutually exclusive.
Three coins are tossed. Describe two events which are mutually exclusive but not exhaustive.
Two dice are thrown. The events A, B and C are as follows:
A: getting an even number on the first die.
B: getting an odd number on the first die.
C: getting the sum of the numbers on the dice ≤ 5.
State true or false: (give reason for your answer).
A and B are mutually exclusive
Two dice are thrown. The events A, B and C are as follows:
A: getting an even number on the first die.
B: getting an odd number on the first die.
C: getting the sum of the numbers on the dice ≤ 5
State true or false: (give reason for your answer)
A and B are mutually exclusive and exhaustive
Two dice are thrown. The events A, B and C are as follows:
A: getting an even number on the first die.
B: getting an odd number on the first die.
C: getting the sum of the numbers on the dice ≤ 5
State true or false: (give reason for your answer)
A and C are mutually exclusive
Given P(A) = `3/5` and P(B) = `1/5`. Find P(A or B), if A and B are mutually exclusive events.
Three coins are tossed. Describe. two events A and B which are mutually exclusive.
Three coins are tossed. Describe. two events A and B which are not mutually exclusive.
A die is thrown twice. Each time the number appearing on it is recorded. Describe the following events:
A = Both numbers are odd.
B = Both numbers are even.
C = sum of the numbers is less than 6
Also, find A ∪ B, A ∩ B, A ∪ C, A ∩ C
Which pairs of events are mutually exclusive?
The numbers 1, 2, 3 and 4 are written separately on four slips of paper. The slips are then put in a box and mixed thoroughly. A person draws two slips from the box, one after the other, without replacement. Describe the following events:
A = The number on the first slip is larger than the one on the second slip.
B = The number on the second slip is greater than 2
C = The sum of the numbers on the two slips is 6 or 7
D = The number on the second slips is twice that on the first slip.
Which pair(s) of events is (are) mutually exclusive?
If A and B be mutually exclusive events associated with a random experiment such that P(A) = 0.4 and P(B) = 0.5, then find
P (A ∩\[\bar{ B } \] ).
If A and B are mutually exclusive events such that P(A) = 0.35 and P(B) = 0.45, find P(A ∩ B)
If A and B are mutually exclusive events such that P(A) = 0.35 and P(B) = 0.45, find P(A ∩ \[\bar{ B } \] )
The probabilities of three mutually exclusive events A, B and C are given by 2/3, 1/4 and 1/6 respectively. The statement
If \[\frac{(1 - 3p)}{2}, \frac{(1 + 4p)}{3}, \frac{(1 + p)}{6}\] are the probabilities of three mutually exclusive and exhaustive events, then the set of all values of p is
If A, B, C are three mutually exclusive and exhaustive events of an experiment such that 3 P(A) = 2 P(B) = P(C), then P(A) is equal to
If A and B are mutually exclusive events then
An experiment has four possible outcomes A, B, C and D, that are mutually exclusive. Explain why the following assignments of probabilities are not permissible:
P(A) = 0.12, P(B) = 0.63, P(C) = 0.45, P(D) = – 0.20
If A, B, C are three mutually exclusive and exhaustive events of an experiment such that 3P(A) = 2P(B) = P(C), then P(A) is equal to ______.
A die is loaded in such a way that each odd number is twice as likely to occur as each even number. Find P(G), where G is the event that a number greater than 3 occurs on a single roll of the die.
If A and B are mutually exclusive events, P(A) = 0.35 and P(B) = 0.45, find P(B′)
If A and B are mutually exclusive events, P(A) = 0.35 and P(B) = 0.45, find P(A ∩ B)
If A and B are mutually exclusive events, P(A) = 0.35 and P(B) = 0.45, find P(A ∩ B′)
One of the four persons John, Rita, Aslam or Gurpreet will be promoted next month. Consequently the sample space consists of four elementary outcomes S = {John promoted, Rita promoted, Aslam promoted, Gurpreet promoted} You are told that the chances of John’s promotion is same as that of Gurpreet, Rita’s chances of promotion are twice as likely as Johns. Aslam’s chances are four times that of John.
Determine P(John promoted)
P(Rita promoted)
P(Aslam promoted)
P(Gurpreet promoted)
One of the four persons John, Rita, Aslam or Gurpreet will be promoted next month. Consequently the sample space consists of four elementary outcomes S = {John promoted, Rita promoted, Aslam promoted, Gurpreet promoted} You are told that the chances of John’s promotion is same as that of Gurpreet, Rita’s chances of promotion are twice as likely as Johns. Aslam’s chances are four times that of John. If A = {John promoted or Gurpreet promoted}, find P(A).
Let E1, E2, E3 be three mutually exclusive events such that P(E1) = `(2 + 3p)/6`, P(E2) = `(2 - p)/8` and P(E3) = `(1 - p)/2`. If the maximum and minimum values of p are p1 and p2, then (p1 + p2) is equal to ______.
If the events A and B are mutually exclusive events such that P(A) = `(3x + 1)/3` and P(B) = `(1 - x)/4`, then the set of possible values of x lies in the interval ______.
