मराठी

If A and B are mutually exclusive events such that P(A) = 0.35 and P(B) = 0.45, find (iv) P( ¯ A ∩ ¯ B ) - Mathematics

Advertisements
Advertisements

प्रश्न

If A and B are mutually exclusive events such that P(A) = 0.35 and P(B) = 0.45, find P(\[\bar{ A } \] ∩  \[\bar{B} \] ) 

 

उत्तर

It is given that A and B are mutually exclusive events.
∴ P(A ∩ B) = 0
Also, P(A) = 0.35 and P(B) = 0.45.

 \[P\left( A \cap B \right) = P\left( A \cup B \right)\]
\[ = 1 - P\left( A \cup B \right)\]
\[ = 1 - 0 . 80\]
\[ = 0 . 20\]

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 33: Probability - Exercise 33.4 [पृष्ठ ६९]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 11
पाठ 33 Probability
Exercise 33.4 | Q 27.4 | पृष्ठ ६९

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

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 three events which are mutually exclusive and exhaustive.


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 and B are mutually exclusive and exhaustive


Events E and F are such that P(not E or not F) = 0.25, State whether E and F are mutually exclusive.


Three coins are tossed. Describe.

(iv) two events A and B which are mutually exclusive but not exhaustive.

 

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 ∪ BA ∩ BA ∪ CA ∩ C
Which pairs of events are mutually exclusive?


Two dice are thrown. The events ABCDE 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.
 Describe the event:
A and BB or CB and CA and EA or FA and F


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:

  1. A and B are mutually exclusive.
  2. A and B are mutually exclusive and exhaustive events.
  3. A and C are mutually exclusive events.
  4. C and D are mutually exclusive and exhaustive events.
  5. C, D and E are mutually exclusive and exhaustive events.
  6. A' and B' are mutually exclusive events.
  7. 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

\[P (\bar{ A } \cap \bar{ B} )\]


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 ( \[\bar{ A} \] ∩ 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 (A ∩\[\bar{ B } \] ).

 

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?


The probability that a person will travel by plane is 3/5 and that he will travel by trains is 1/4. What is the probability that he (she) will travel by plane or train?


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 ∩ 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 AB and are given by 2/3, 1/4 and 1/6 respectively. The statement


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) =

 

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 and B are any two events having P(A ∪ B) = `1/2` and P`(barA) = 2/3`, then the probability of `barA ∩ B` is ______.


If A and B are mutually exclusive events, P(A) = 0.35 and P(B) = 0.45, find P(A′)


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).


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 ______.


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 ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×