Advertisements
Advertisements
प्रश्न
A sample space consists of 9 elementary events E1, E2, E3, ..., E9 whose probabilities are
P(E1) = P(E2) = 0.08, P(E3) = P(E4) = P(E5) = 0.1, P(E6) = P(E7) = 0.2, P(E8) = P(E9) = 0.07
Suppose A = {E1, E5, E8}, B = {E2, E5, E8, E9}
Using the addition law of probability, find P(A ∪ B).
उत्तर
Let S be the sample space of the elementary events.
S = {E1, E2, E3, ..., E9}
Given:
A = {E1, E5, E8}
B = {E2, E5, E8, E9}
P(E1) = P(E2) = 0.08, P(E3) = P(E4) = P(E5) = 0.1, P(E6) = P(E7) = 0.2, P(E8) = P(E9) = 0.07
By the addition law of probability, we have
P(A ∪ B) = P(A) + P(B) − P(A ∩ B)
= 0.25 + 0.32 − 0.17
= 0.40
Notes
The solution of the problem is provided by taking P(E5) = 0.1. This information is missing in the question as given in the book.
APPEARS IN
संबंधित प्रश्न
Describe the sample space for the indicated experiment: A coin is tossed and then a die is rolled only in case a head is shown on the coin.
If a coin is tossed three times (or three coins are tossed together), then describe the sample space for this experiment.
Write the sample space for the experiment of tossing a coin four times.
What is the total number of elementary events associated to the random experiment of throwing three dice together?
In a random sampling three items are selected from a lot. Each item is tested and classified as defective (D) or non-defective (N). Write the sample space of this experiment.
An experiment consists of boy-girl composition of families with 2 children.
What is the sample space if we are interested in knowing whether it is a boy or girl in the order of their births?
There are three coloured dice of red, white and black colour. These dice are placed in a bag. One die is drawn at random from the bag and rolled its colour and the number on its uppermost face is noted. Describe the sample space for this experiment.
A bag contains one white and one red ball. A ball is drawn from the bag. If the ball drawn is white it is replaced in the bag and again a ball is drawn. Otherwise, a die is tossed. Write the sample space for this experiment.
A box contains 1 white and 3 identical black balls. Two balls are drawn at random in succession without replacement. Write the sample space for this experiment.
An experiment consists of rolling a die and then tossing a coin once if the number on the die is even. If the number on the die is odd, the coin is tossed twice. Write the sample space for this experiment.
A card is drawn at random from a pack of 52 cards. Find the probability that the card drawn is black and a king
A card is drawn at random from a pack of 52 cards. Find the probability that the card drawn is not a diamond card
From a deck of 52 cards, four cards are drawn simultaneously, find the chance that they will be the four honours of the same suit.
Tickets numbered from 1 to 20 are mixed up together and then a ticket is drawn at random. What is the probability that the ticket has a number which is a multiple of 3 or 7?
A bag contains 7 white, 5 black and 4 red balls. If two balls are drawn at random, find the probability that one ball is black and the other red
A bag contains 6 red, 4 white and 8 blue balls. If three balls are drawn at random, find the probability that two are blue and one is red
Five cards are drawn from a pack of 52 cards. What is the chance that these 5 will contain:
(i) just one ace
Two balls are drawn at random from a bag containing 2 white, 3 red, 5 green and 4 black balls, one by one without, replacement. Find the probability that both the balls are of different colours.
20 cards are numbered from 1 to 20. One card is drawn at random. What is the probability that the number on the cards is not a multiple of 4?
20 cards are numbered from 1 to 20. One card is drawn at random. What is the probability that the number on the cards is not a multiple of 6?
An urn contains 7 white, 5 black and 3 red balls. Two balls are drawn at random. Find the probability that both the balls are red .
A sample space consists of 9 elementary events E1, E2, E3, ..., E9 whose probabilities are
P(E1) = P(E2) = 0.08, P(E3) = P(E4) = P(E5) = 0.1, P(E6) = P(E7) = 0.2, P(E8) = P(E9) = 0.07
Suppose A = {E1, E5, E8}, B = {E2, E5, E8, E9}
List the composition of the event A ∪ B, and calculate P(A ∪ B) by addting the probabilities of elementary events.
A sample space consists of 9 elementary events E1, E2, E3, ..., E9 whose probabilities are
P(E1) = P(E2) = 0.08, P(E3) = P(E4) = P(E5) = 0.1, P(E6) = P(E7) = 0.2, P(E8) = P(E9) = 0.07
Suppose A = {E1, E5, E8}, B = {E2, E5, E8, E9}
Calculate \[P\left( \bar{ B} \right)\] from P(B), also calculate \[P\left( \bar{ B } \right)\] directly from the elementary events of \[\bar{ B } \] .
A single letter is selected at random from the word 'PROBABILITY'. What is the probability that it is a vowel?
If the letters of the word 'MISSISSIPPI' are written down at random in a row, what is the probability that four S's come together.
What is the probability that the 13th days of a randomly chosen month is Friday?
If A and B are two independent events such that \[P (A \cap B) = \frac{1}{6}\text{ and } P (A \cap B) = \frac{1}{3},\] then write the values of P (A) and P (B).
One card is drawn from a pack of 52 cards. The probability that it is the card of a king or spade is
Two dice are thrown simultaneously. The probability of obtaining a total score of 5 is
The probability of getting a total of 10 in a single throw of two dices is
A pack of cards contains 4 aces, 4 kings, 4 queens and 4 jacks. Two cards are drawn at random. The probability that at least one of them is an ace is
Three digit numbers are formed using the digits 0, 2, 4, 6, 8. A number is chosen at random out of these numbers. What is the probability that this number has the same digits?
An ordinary deck of cards contains 52 cards divided into four suits. The red suits are diamonds and hearts and black suits are clubs and spades. The cards J, Q, and K are called face cards. Suppose we pick one card from the deck at random. What is the sample space of the experiment?
How many two-digit positive integers are multiples of 3?
