Advertisements
Advertisements
Question
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.
Solution
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
RELATED QUESTIONS
A die is rolled. Let E be the event “die shows 4” and F be the event “die shows even number”. Are E and F mutually exclusive?
Three coins are tossed. Describe two events, which are not 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
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 = B'
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.
Three coins are tossed. Describe.
(iv) two events A and B which are mutually exclusive but not exhaustive.
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
\[P (\bar{ A } \cap \bar{ B} )\]
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 ∩\[\bar{ B } \] ).
Given two mutually exclusive events A and B such that P(A) = 1/2 and P(B) = 1/3, find P(A or B).
A box contains 10 white, 6 red and 10 black balls. A ball is drawn at random from the box. What is the probability that the ball drawn is either white or red?
If A and B are mutually exclusive events such that P(A) = 0.35 and P(B) = 0.45, find P(A ∪ B)
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 S is the sample space and P(A) = \[\frac{1}{3}\] P(B) and S = A ∪ B, where A and B are two mutually exclusive events, then P (A) =
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
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
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) = `9/120`, P(B) = `45/120`, P(C) = `27/120`, P(D) = `46/120`
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 ______.
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).
If A and B are mutually exclusive events, then ______.
The probability of happening of an event A is 0.5 and that of B is 0.3. If A and B are mutually exclusive events, then the probability of neither A nor B is ______.
| Column A | Column B |
| (a) If E1 and E2 are the two mutually exclusive events | (i) E1 ∩ E2 = E1 |
| (b) If E1 and E2 are the mutually exclusive and exhaustive events | (ii) (E1 – E2) ∪ (E1 ∩ E2) = E1 |
| (c) If E1 and E2 have common outcomes, then | (iii) E1 ∩ E2 = Φ, E1 ∪ E2 = S |
| (d) If E1 and E2 are two events such that E1 ⊂ E2 | (iv) E1 ∩ E2 = Φ |
