Advertisements
Advertisements
Question
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?
Solution
We have two events such that
A = a person will travel by plane
and B = a person will travel by train.
i.e.
P (A ∩ B) = 0
By addition theorem, we have:
P (A ∪ B) = P(A) + P (B) - P (A ∩ B)
= \[\frac{3}{5} + \frac{1}{4} - 0 = \frac{12 + 5}{20} = \frac{17}{20}\]
Hence, required probability = \[\frac{17}{20}\]
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?
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.
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
Given P(A) = `3/5` and P(B) = `1/5`. Find P(A or B), if A and B are mutually exclusive events.
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. two events A and B which are mutually exclusive.
Three coins are tossed. Describe. two events A and B which are not mutually exclusive.
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.
Describe the event:
A and B, B or C, B and C, A and E, A or F, A and F
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
\[P (\bar{ A } \cap \bar{ B} )\]
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.
A box contains 30 bolts and 40 nuts. Half of the bolts and half of the nuts are rusted. If two items are drawn at random, what is the probability that either both are rusted or both are bolts?
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 ∩ \[\bar{ B } \] )
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′)
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, 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 ______.
