English

A Card is Drawn at Random from a Pack of 52 Cards. Find the Probability that the Card Drawn Is:(Viii) a Diamond Card - Mathematics

Advertisements
Advertisements

Question

A card is drawn at random from a pack of 52 cards. Find the probability that the card drawn is a diamond card

Solution

Let S denote the sample space.
Then, n(S) = 52

 Let E8 = event of drawing a diamond card.
         There are 13 diamond cards in a pack of 52 cards, out of which one diamond can be drawn in 13C1 .
         ∴ n (E8) = 13

\[P\left( E_8 \right) = \frac{n\left( E_8 \right)}{n\left( S \right)} = \frac{13}{52} = \frac{1}{4}\]

 

shaalaa.com
  Is there an error in this question or solution?
Chapter 33: Probability - Exercise 33.3 [Page 46]

APPEARS IN

RD Sharma Mathematics [English] Class 11
Chapter 33 Probability
Exercise 33.3 | Q 10.08 | Page 46

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

Describe the sample space for the indicated experiment: A coin is tossed four times.


An experiment consists of recording boy-girl composition of families with 2 children.

(i) What is the sample space if we are interested in knowing whether it is a boy or girl in the order of their births?

(ii) What is the sample space if we are interested in the number of girls in the family?


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 coin is tossed and then a die is thrown. Describe the sample space for this experiment.


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.


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.


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.

 

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.
(i) Which pairs of events are mutually exclusive?

 


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 drawn at random from a pack of 52 cards. Find the probability that the card drawn is either a black card 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


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.


A bag contains 6 red, 4 white and 8 blue balls. if three balls are drawn at random, find the probability that one is red, one is white and one is blue.

 

The letters of the word' CLIFTON' are placed at random in a row. What is the chance that two vowels 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?


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 greater than 12?


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?


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?


Five cards are drawn from a well-shuffled pack of 52 cards. Find the probability that all the five cards are hearts.


A bag contains tickets numbered from 1 to 20. Two tickets are drawn. Find the probability that  both the tickets have prime numbers on them


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. 


Suppose an integer from 1 through 1000 is chosen at random, find the probability that the integer is a multiple of 2 or a multiple of 9.


A sample space consists of 9 elementary events E1E2E3, ..., 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 = {E1E5E8}, B = {E2E5E8, E9}   

 List the composition of the event A ∪ B, and calculate P(A ∪ B) by addting the probabilities of elementary events.


n (≥ 3) persons are sitting in a row. Two of them are selected. Write the probability that they are together.

 

A single letter is selected at random from the word 'PROBABILITY'. What is the probability that it is a vowel?


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.


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


Two dice are thrown simultaneously. The probability of obtaining total score of seven is


The probability of getting a total of 10 in a single throw of two dices is


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


Without repetition of the numbers, four digit numbers are formed with the numbers 0, 2, 3, 5. The probability of such a number divisible by 5 is


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?


A single letter is selected at random from the word 'PROBABILITY'. The probability that it is a vowel is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×