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महाराष्ट्र राज्य शिक्षण मंडळएस.एस.सी (इंग्रजी माध्यम) इयत्ता १० वी

A Two Digit Number is to Be Formed from the Digits 0,1,2,3,4, Without Repetition of the Digits. Find the Probability that the Number So Formed is a Prime Number - Algebra

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प्रश्न

A two digit number is to be formed from the digits 0,1,2,3,4,
without repetition of the digits. Find the probability that the number so
formed is a prime number

उत्तर

The sample space,
S = {10,12,13,14,20,21,23,24,30,31,32,34,40,41,42,43}
∴ n(S) = 16
Let A be the event that the number is a prime.
∴ A = {13,23,31,41,43}
∴ n(A) = 5
∴ `P(A) = (n(A))/(n(S)) = 5/16`

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2018-2019 (March) Balbharati Model Question Paper Set 2

संबंधित प्रश्‍न

‘A coin is tossed’. Write the sample space ‘S’.


A die is thrown, find the probability of the event of getting a number less than 3.


In a single throw of a dice, find the probability of getting a number not greater than 4.


In a single throw of a dice, find the probability of getting 5.


In a single throw of a dice, find the probability of getting 8.


For the following experiment write sample space ‘S’ and number of sample points n(S).

Two-digit numbers are formed using digits 2, 3 and 5 without repeating a digit.


The arrow is rotated and it stops randomly on the disc. Find out on which colour it may stop.


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).

From three men and two women, environment committee of two persons is to be formed.
Condition for event A : There must be at least one woman member.
Condition for event B : One man, one woman committee to be formed.
Condition for event C : There should not be a woman member.


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 at least 10.


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.


There are 15 tickets in a box, each bearing one of the numbers from 1 to 15. One ticket is drawn at random from the box. Find the probability of event that the ticket drawn - shows a number which is a multiple of 5.


Do the following activity -

Activity II : Decide the sample space yourself and fill in the following boxes.


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.


Write the sample space if two coins are tossed.


Two dice are thrown, find the probability of getting
(1) The sum of numbers on their upper faces is at least 10.
(2) The sum of the numbers on their upper faces is divisible by 5.
(3) The number on the upper face of the first die is greater than the number on the upper face of the second die.


Write a sample space when a die is thrown


Two coins are tossed simultaneously. Write the sample space (S) and expected sample points in the given events by completing the activity.

  1. Event A: to get at least one head.
  2. Event B: to get no head.

Activity: Let ‘S’ be the sample space, when two coins are tossed simultaneously.

∴ S = `{square, HT, TH, square}`

i. Event A: to get at least one head.

∴ A = `{HH, square, TH}`

ii. Event B: to get no head.

∴ B = `{square}`.


Two coins are tossed simultaneously. Complete the following activity to write the sample space and the given events A and B in the set form:

Event A: To get at least one head.

Event B: To get no head.

Activity:

Two coins are tossed simultaneously.

∴ Sample space is

S = `{square, HT, TH, square}`

Event A: To get at least one head.

∴ A = `{square, HT, TH}`

Event B: To get no head.

∴ B = `{square}`


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