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}
Compute P(A), P(B) and 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
P(A) = P(E1) + P(E5) + P(E8) = 0.08 + 0.1 + 0.07 = 0.25
P(B) = P(E2) + P(E5) + P(E8) + P(E9) = 0.08 + 0.1 + 0.07 + 0.07 = 0.32
Now, A ∩ B = {E5, E8}
∴ P(A ∩ B) = P(E5) + P(E8) = 0.1 + 0.07 = 0.17
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
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.
A coin is tossed and then a die is thrown. Describe the sample space for this experiment.
An experiment consists of tossing a coin and then tossing it second time if head occurs. If a tail occurs on the first toss, then a die is tossed once. Find the sample space.
A coin is tossed. If it shows tail, we draw a ball from a box which contains 2 red 3 black balls; if it shows head, we throw a die. Find the sample space of this experiment.
A coin is tossed twice. If the second draw results in a head, a die is rolled. Write the sample space for this experiment.
A bag contains 4 identical red balls and 3 identical black balls. The experiment consists of drawing one ball, then putting it into the bag and again drawing a ball. What are the possible outcomes of the experiment?
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?
A die is thrown repeatedly until a six comes up. What is the sample space for this experiment.
List all events associated with the random experiment of tossing of two coins. How many of them are elementary events.
A card is picked up from a deck of 52 playing cards.
What is the sample space of the experiment?
A card is drawn at random from a pack of 52 cards. Find the probability that the card drawn is a black king
A card is drawn at random from a pack of 52 cards. Find the probability that the card drawn is a jack, queen or a king
A card is drawn at random from a pack of 52 cards. Find the probability that the card drawn is spade or an ace
A card is drawn at random from a pack of 52 cards. Find the probability that the card drawn is a diamond card
A bag contains 7 white, 5 black and 4 red balls. If two balls are drawn at random, find the probability that both the balls are white
Five cards are drawn from a pack of 52 cards. What is the chance that these 5 will contain:
(i) just one ace
The face cards are removed from a full pack. Out of the remaining 40 cards, 4 are drawn at random. what is the probability that they belong to different suits?
There are four men and six women on the city councils. If one council member is selected for a committee at random, how likely is that it is a women?
Find the probability that in a random arrangement of the letters of the word 'SOCIAL' vowels come together.
The letters of the word 'FORTUNATES' are arranged at random in a row. What is the chance that the two 'T' come together.
A committee of two persons is selected from two men and two women. What is the probability that the committee will have one man?
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 divisible by 5?
A class consists of 10 boys and 8 girls. Three students are selected at random. What is the probability that the selected group has at most one girl?
A bag contains tickets numbered from 1 to 20. Two tickets are drawn. Find the probability that on one there is a prime number and on the other there is a multiple of 4.as
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).
What is the probability that the 13th days of a randomly chosen month is Friday?
A card is drawn at random from a pack of 100 cards numbered 1 to 100. The probability of drawing a number which is a square is
Six boys and six girls sit in a row randomly. The probability that all girls sit together 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
6 boys and 6 girls sit in a row at random. The probability that all the girls sit together is
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 event that the chosen card is a black face card?
How many two-digit positive integers are multiples of 3?
The probability that a randomly chosen 2 × 2 matrix with all the entries from the set of first 10 primes, is singular, is equal to ______.
