Advertisements
Advertisements
प्रश्न
Two dice are rolled simultaneously. The probability that they show different faces is
विकल्प
\[\frac{2}{3}\]
\[\frac{1}{6}\]
\[\frac{1}{3}\]
\[\frac{5}{6}\]
उत्तर
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
संबंधित प्रश्न
Two coins are tossed simultaneously. Write the sample space (S), n(S), the following event A
using set notation and n(A), where ‘A is the event of getting at least one head.’
Two different dice are thrown together. Find the probability that the numbers obtained have
1) even sum, and
2) even product.
In a hockey team, there are 6 defenders, 4 offenders, and 1 goalee. Out of these, one player is to be selected randomly as a captain. Find the probability of the selection that – The goalee will be selected.
The faces of a die bear numbers 0, 1, 2, 3, 4, 5. If the die is rolled twice, then find the probability that the product of digits on the upper face is zero.
Cards each marked with one of the numbers 4, 5, 6, ..., 20 are placed in a box and mixed thoroughly. One card is drawn at random from the box. What is the probability of getting an even number?
A number is selected at random from the numbers 3, 5, 5, 7, 7, 7, 9, 9, 9, 9 The probability that the selected number is their average is
If P(E) = 0.05, then P(not E) =
A number x is chosen at random from the numbers −3, −2, −1, 0, 1, 2, 3 the probability that | x | < 2 is
In a single throw of a pair of dice, the probability of getting the sum a perfect square is
If a die is rolled, what is the probability that number appearing on upper face is less than 2?
Five cards − the ten, jack, queen, king and ace of diamonds are well shuffled with their faces downwards. One card is then picked up at random. If the queen is drawn and put aside and a second card is drawn, find the probability that the second card is
- an ace,
- a queen.
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?
From a well-shuffled deck of 52 cards, one card is drawn at random. What is the probability of getting a queen?
Three different coins are tossed simultaneously. Find the probability of getting exactly one head.
A coin is tossed twice. Find the probability of getting: two heads
From 10 identical cards, numbered 1, 2, 3, ……, 10, one card is drawn at random. Find the probability that the number on the card drawn is a multiple of
2 or 3
A coin is tossed once. Find the probability of getting a head
You are walking along a street. If you just choose a stranger crossing you, what is the probability that his next birthday will fall on a Sunday?
Two dice are rolled, find the probability that the sum is less than 13
There are 1000 sealed envelopes in a box, 10 of them contain a cash prize of Rs 100 each, 100 of them contain a cash prize of Rs 50 each and 200 of them contain a cash prize of Rs 10 each and rest do not contain any cash prize. If they are well shuffled and an envelope is picked up out, what is the probability that it contains no cash prize?
