Advertisements
Advertisements
Question
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
Options
1/5
3/16
9/20
1/9
Solution
\[\frac{9}{20}\] We have:
P(both are aces) = \[\frac{{}^4 C_2}{{}^{16} C_2} =\]
\[\frac{4}{16} \times \frac{3}{15} = \frac{1}{20}\] P(one is ace) = \[\frac{{}^4 C_1 \times^{12} C_1}{C {{}^{16}}_2} = \frac{2}{5}\]
∴ P(at least one is ace) = \[\frac{1}{20} + \frac{2}{5} = \frac{9}{20}\]
APPEARS IN
RELATED QUESTIONS
2 boys and 2 girls are in Room X, and 1 boy and 3 girls in Room Y. Specify the sample space for the experiment in which a room is selected and then a person.
A box contains 1 red and 3 identical white balls. Two balls are drawn at random in succession without replacement. Write the sample space for this experiment.
A coin is tossed. If the out come is a head, a die is thrown. If the die shows up an even number, the die is thrown again. What is the sample space for the 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 coin is tossed once. Write its sample space
If a coin is tossed two times, describe the sample space associated to 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. 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.
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. Find the total number of elementary events and also the total number events associated with the random 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.
(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
In shuffling a pack of 52 playing cards, four are accidently dropped; find the chance that the missing cards should be one from each suit.
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 both the balls are white
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 of the same colour.
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
The letters of the word' CLIFTON' are placed at random in a row. What is the chance that two vowels come together?
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 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 girls?
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
Two cards are drawn from a well shuffled pack of 52 cards. Find the probability that either both are black or both are kings.
In a large metropolitan area, the probabilities are 0.87, 0.36, 0.30 that a family (randomly chosen for a sample survey) owns a colour television set, a black and white television set, or both kinds of sets. What is the probability that a family owns either any one or both kinds of sets?
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 \[\bar{ B } \] .
What is the probability that a leap year will have 53 Fridays or 53 Saturdays?
Three dice are thrown simultaneously. What is the probability of getting 15 as the sum?
Four persons are selected at random out of 3 men, 2 women and 4 children. The probability that there are exactly 2 children in the selection 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
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?
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?
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?
Five horses are in a race. Mr. A selects two of the horses at random and bets on them. The probability that Mr. A selected the winning horse is ______.
