Advertisements
Advertisements
Question
A black die and a white die are thrown at the same time. Write all the possible outcomes. What is the probability?
that the difference of the numbers appearing on the top of two dice is 2.
Solution
A pair of dice is thrown
TO FIND: Probability of the following:
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 is `6^2=36`
Favourable outcomes for getting the difference of the numbers as 2 are
(1, 3), (3, 1), (2, 4), (4, 2), (3, 5), (5, 3), (4, 6), (6, 4)
Thus, the number of favourable outcomes are 8.
∴ P(getting the difference of the numbers as 2) =\[\frac{\text{ Favourable number of outcomes }}{\text{ Total number of outcomes }} = \frac{8}{36} = \frac{2}{9}\]
APPEARS IN
RELATED QUESTIONS
A letter of English alphabet is chosen at random. Determine the probability that the chosen letter is consonant.
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.
Two different coins are tossed simultaneously. The probability of getting at least one head is
(A)`1/2`
(B)`1/8`
(C)`3/4`
(D)`7/8`
Two different dice are rolled simultaneously. Find the probability that the sum of numbers appearing on the two dice is 10 ?
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.
In a bag there are 44 identical cards with figure of circle or square on them. There are 24 circles, of which 9 are blue and rest are green and 20 squares of which 11 are blue and rest are green. One card is drawn from the bag at random. Find the probability that it has the figure of green colour
The probability of guessing the correct answer to a certain test questions is\[\frac{x}{12}\] If the probability of not guessing the correct answer to this question is\[\frac{ 2}{3}\] then x =
The probability that a number selected at random from the numbers 1, 2, 3, ..., 15 is a multiple of 4, is
A coin is tossed once. What is the probability of getting a tail?
A card is drawn at random from a well-shuffled pack of 52 cards. Find the probability that the drawn card is neither a king nor a queen.
A card is drawn from a well-shuffled pack of 52 cards. Find the probability of getting a black king.
A game of chance consists of spinning an arrow which is equally likely to come to rest pointing to one of the numbers 1, 2, 3,..., 12 as shown in the figure. What is the probability that it will point to a prime number ?
All kings, queens and aces are removed from a pack of 52 cards. The remaining cards are well-shuffled and then a card is drawn from it. Find the probability that the drawn card is a red card.
From the same place at 7 a.m. A started walking in the north at a speed of 4 km/hr. after 1 hour, B started cycling in the east at a speed of 8 km/hr. at what time will they be at a distance of 20 km apart from each other?
In a single throw of a die, find the probability that the number:
(i) will be an even number.
(ii) will be an odd number.
(iii) will not be an even number.
Which of the following can not be the probability of an event?
(i)`2/7`
(ii)3.8
(iii) 37%
(iv) -0.8
(v) 0.8
(vi) `(-2)/5`
(vii) `7/8`
Frame two problems in calculating probability, based on the spinner shown here.
A dice is rolled once. What is the probability that the number on top will be a factor of 36
