Advertisements
Advertisements
प्रश्न
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).
उत्तर
Let E1, E2, E3 and E4 be the events that John promoted, Rita promoted, Aslam promoted and Gurpreet promoted respectively.
∴ Sample space S = {E1, E2, E3, E4}
Given that probability of John’s promotion is same as that of Gurpreet
∴ P(E1) = P(E4)
Rita’s chances of promotion are twice as likely as John
∴ P(E2) = 2P(E1)
And Aslam’s chances of promotion are 4 times that of John
∴ P(E3) = 4P(E1)
Since, the sum of all the probabilities = 1
∴ P(E1) + P(E2) + P(E3) + P(E4) = 1
⇒ P(E1) + 2P(E1) + 4P(E1) + P(E1) = 1
⇒ 8P(E1) = 1
⇒ P(E1) = `1/8`
P(John promoted or Gurpreet promoted) = P(E1 ∪ E4)
⇒ P(E1 ∪ E4) = P(E1) + P(E4) – P(E1 ∩ E4)
= `1/8 + 1/8 - 0` ......[∵ P(E1 ∩ E4) = 0]
= `1/4`
APPEARS IN
संबंधित प्रश्न
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?
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 three 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 = B'
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
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' , B' ,C are mutually exclusive and exhaustive.
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.
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 ∪ 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 ( \[\bar{ A} \] ∩ 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).
From a well shuffled deck of 52 cards, 4 cards are drawn at random. What is the probability that all the drawn cards are of the same colour.
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?
In a race, the odds in favour of horses A, B, C, D are 1 : 3, 1 : 4, 1 : 5 and 1 : 6 respectively. Find probability that one of them wins the race.
If A and B are mutually exclusive events such that P(A) = 0.35 and P(B) = 0.45, find P(A ∩ \[\bar{ B } \] )
If A and B are mutually exclusive events then
If A and B are any two events having P(A ∪ B) = `1/2` and P`(barA) = 2/3`, then the probability of `barA ∩ B` is ______.
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(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)
| 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 |
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 ______.
