Advertisements
Advertisements
प्रश्न
A typical PIN (personal identification number) is a sequence of any four symbols chosen from the 26 letters in the alphabet and the ten digits. If all PINs are equally likely, what is the probability that a randomly chosen PIN contains a repeated symbol?
उत्तर
A PIN is a sequence of four symbols selected from 36 (26 letters + 10 digits) symbols.
By the fundamental principle of counting
There are 36 × 36 × 36 × 36 = 364 = 1,679,616 PINs in all.
When repetition is not allowed the multiplication rule can be applied to conclude that there are 36 × 35 × 34 × 33 = 1,413,720 different PINs
The number of PINs that contain at least one repeated symbol = 1,679,616 – 1,413,720 = 2,65,896
Thus, the probability that a randomly chosen PIN contains a repeated symbol is
`(265, 896)/(1, 679, 616)` = 1.583
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.
A coin is tossed. If it shows a tail, we draw a ball from a box which contains 2 red and 3 black balls. If it shows head, we throw a die. Find the sample space for this experiment.
A die is thrown repeatedly until a six comes up. What is the sample space for this experiment?
What is the total number of elementary events associated to the random experiment of throwing three dice together?
A coin is tossed twice. If the second throw results in a tail, a die is thrown. Describe the sample space for 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.
Three coins are tossed once. Describe the events associated with this random experiment:
A = Getting three heads
B = Getting two heads and one tail
C = Getting three tails
D = Getting a head on the first coin.
(ii) Which events are elementary events?
Three coins are tossed once. Describe the events associated with this random experiment:
A = Getting three heads
B = Getting two heads and one tail
C = Getting three tails
D = Getting a head on the first coin.
(iii) Which events are compound 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 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
A card is drawn at random from a pack of 52 cards. Find the probability that the card drawn is not an ace
A card is drawn at random from a pack of 52 cards. Find the probability that the card drawn is not a black 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
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?
Find the probability that in a random arrangement of the letters of the word 'UNIVERSITY', the two I's do not come together.
A committee of two persons is selected from two men and two women. What is the probability that the committee will have no 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 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 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 all boys?
An urn contains 7 white, 5 black and 3 red balls. Two balls are drawn at random. Find the probability that one ball is white.
Two cards are drawn from a well shuffled pack of 52 cards. Find the probability that either both are black or both are kings.
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).
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).
A single letter is selected at random from the word 'PROBABILITY'. What is the probability that it is a vowel?
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 together. The probability that at least one will show its digit greater than 3 is
A die is rolled, then the probability that a number 1 or 6 may appear is
Six boys and six girls sit in a row randomly. The probability that all girls sit together is
Three of the six vertices of a regular hexagon are chosen at random. What is the probability that the triangle with these vertices is equilateral?
