Advertisements
Advertisements
प्रश्न
If two dice are rolled simultaneously, find the probability of the following event.
The digit on the first die is greater than the digit on second die.
उत्तर
Sample Space (S) = `{[(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)]}`
∴ n(S) = 36
Event C: digit on the first die is greater than the digit on second die
C = {(2,1), (3,1), (3,2), (4,1), (4,2), (4,3), (5,1), (5,2), (5,3), (5,4), (6,1), (6,2), (6,3), (6,4), (6,5)}
∴ n(C) = 15
`therefore P (C) =(n(C))/(n(S))`
`=15/36`
`=5/12`
Hence, the probability that digit on the first die is greater than the digit on second die is `=5/12`
APPEARS IN
संबंधित प्रश्न
A die is thrown. If A is the event that the number on upper face is less than 5, then write sample space and event A in set notation.
There are 15 tickets bearing the numbers from 1 to 15 in a bag and one ticket is drawn from this bag at random. Write the sample space (S) and n(S).
In a single throw of a dice, find the probability of getting a number greater than 4.
In a single throw of a dice, find the probability of getting a number less than or equal to 4.
In a single throw of a dice, find the probability of getting 8.
In a single throw of a dice, find the probability of getting a number less than 8.
A dice is thrown once. Find the probability of getting a number between 3 and 8.
A dice is thrown once. Find the probability of getting an even number or a multiple of 3.
For the following experiment write sample space ‘S’ and number of sample points n(S).
One coin and one die are thrown simultaneously.
In the month of March 2019, Find the days on which the date is a multiple of 5. (see the given page of the calender)
Write sample space ‘S’ and number of sample point n(S) for the following experiment. Also write events A, B, C in the set form and write n(A), n(B), n(C).
One die is rolled,
Event A : Even number on the upper face.
Event B : Odd number on the upper face.
Event C : Prime number on the upper face.
Write sample space ‘S’ and number of sample point n(S) for the following experiment. Also write events A, B, C in the set form and write n(A), n(B), n(C).
One coin and one die are thrown simultaneously.
Condition for event A : To get head and an odd number.
Condition for event B : To get a head or tail and an even number.
Condition for event C : Number on the upper face is greater than 7 and tail on the coin.
If two dice are rolled simultaneously, find the probability of the following event. The sum of the digits on the upper faces is 33.
250 lottery tickets were sold and there are 5 prizes on these tickets. If Kunal has purchased one lottery ticket, what is the probability that he wins a prize?
Two coins are tossed simultaneously. Write the sample space ‘S’.
In the following experiment write the sample space S, Number of sample points n(S), write the event P in set form and find n(P):
Form two-digit numbers using the digit 0, 1, 2, 3, 4, without repeating the digits, P is the event, that the number so formed is even.
A die is thrown. Write the sample space. If P is the event of getting an odd number, then write the event P using set notation.
Write a sample space if two coins are tossed simultaneously
Write a sample space when a die is thrown
Assertion (A): A die is thrown once and the probability of getting an even number is `2/3`.
Reason (R): The sample space for even numbers on a die is {2, 4, 6}.
