Advertisements
Advertisements
Question
Two dice are rolled simultaneously. The probability that they show different faces is
Options
\[\frac{2}{3}\]
\[\frac{1}{6}\]
\[\frac{1}{3}\]
\[\frac{5}{6}\]
Solution
A pair of dice is thrown
TO FIND: Probability of getting different faces
Let us first write the all possible events that can occur
(1,1), (1,2), (1,3), (1,4), (1,5), (1,6),
(2,1), (2,2), (2,3), (2,4), (2,5), (2,6),
(3,1), (3,2), (3,3), (3,4), (3,5), (3,6),
(4,1), (4,2), (4,3), (4,4), (4,5), (4,6),
(5,1), (5,2), (5,3), (5,4), (5,5), (5,6),
(6,1), (6,2), (6,3), (6,4), (6,5), (6,6),
Hence total number of events `6^2=36`
Favorable events i.e. getting different faces of both dice are
(1,2), (1,3), (1,4), (1,5), (1,6),
(2,1), (2,3), (2,4), (2,5), (2,6),
(3,1), (3,2), (3,4), (3,5), (3,6),
(4,1), (4,2), (4,3), (4,5), (4,6),
(5,1), (5,2), (5,3), (5,4), (5,6),
(6,1), (6,2), (6,3), (6,4), (6,5),
Hence total number of favorable events i.e. getting different faces of both dice is 30
`"We know that PROBABILITY" = " Number of favourablr event"/"Total number of event"`
Hence probability of getting different faces of both dice is `30/36=5/6`
APPEARS IN
RELATED QUESTIONS
Two digit numbers are formed using the digits 0, 1, 2, 3, 4, 5 where digits are not repeated.
P is the event that the number so formed is even.
Q is the event that the number so formed is greater than 50.
R is the event that the number so formed is divisible by 3.
Then write the sample space S and events P, Q, R using set notation.
The probability that a number selected at random from the numbers 1, 2, 3, ..., 15 is a multiple of 4, is
`(A)4/15`
`(B)2/15`
`(C)1/5`
`(D)1/3`
A box contains cards bearing numbers from 6 to 70. If one card is drawn at random from the box, find the probability that it bears
(i) a one digit number.
(ii) a number divisible by 5.
(iii) an odd number less than 30.
(iv) a composite number between 50 and 70.
A die is tossed once. Find the probability of getting an even number or a multiple of 3 ?
Which number cannot represent a probability?
Choose the correct alternative answer for the following question.
There are 40 cards in a bag. Each bears a number from 1 to 40. One card is drawn at random. What is the probability that the card bears a number which is a multiple of 5 ?
The king, queen and jack of clubs are removed form a deck of 52 playing cards and the remaining cards are shuffled. A card is drawn from the remaining cards. Find the probability of getting a card of a queen of diamond.
All red face cards are removed from a pack of playing cards. The remaining cards are well shuffled and then a card is drawn at random from them. Find the probability that the drawn card is a red card
A bag contains 3 red and 5 black balls. A ball is drawn at random from the bag. What is the probability that the ball drawn is not red.
The probability that a number selected at random from the numbers 1, 2, 3, ..., 15 is a multiple of 4, is
In a family of 3 children, the probability of having at least one boy is
A box contains 80 discs, which are numbered from 1 to 80. If one disc is drawn at random from the box, find the probability that it bears a perfect square number.
A die is thrown once. The probability of getting an even number is
A bag contains 4 red and 6 black balls. A ball is taken out of the bag at random. What is the probability of getting a black ball?
Cards numbered 7 to 40 were put in a box. Poonam selects a card at random. What is the probability that Poonam selects a card which is a multiple of 7?
A coin is tossed twice. Find the probability of getting: exactly one head
Two coins are tossed together. What is the probability of getting:
(i) at least one head
(ii) both heads or both tails.
Two coins are tossed together. Find the probability of getting: at least one head
A die is thrown once. Find the probability of getting:
a number greater than 3
A letter of English alphabets is chosen at random. Determine the probability that the letter is a consonant.
