6. A bag contains 100 cards numbered 1, 2, 3, ..., 98, 99, 100. A card is drawn at random from the bag. Find the probability that the number on the card is
(i) a number less than 30 (ii) a prime number less than 19
(iii) a prime number greater than 83
(iv) a number which is square of some natural number.
Answers
Answer:
Step-by-step explanation:
(i) Numbers less than 30 are 29,28,..3,2,1.
There are total 29 numbers. So probability of getting such number is
⇒ 29/100
If you asked for PRIME numbers, there are 10 prime numbers less than 30. Probability = 10/100 = 1/10
(ii) Prime numbers less than 19 are 17,13,11,7,5,3,2. (1 is not prime number)
There are total 7 numbers. So probability of getting such number is
⇒ 7/100
(iii) Prime numbers greater than 83 are 89 and 97.
There are total 2 numbers. So probability of getting such number is
⇒ 2/100 = 1/50
(iv) Required numbers are 1, 4, 9, 16, 25, 36, 49, 64, 81, 100 or we say 1²,2²,3²,4²,5²,6²,7²,8²,9²,10². (11²>100, so we won't include numbers greater than 11).
There are total 10 numbers. So probability of getting such number is
⇒ 10/100 = 1/10
Answer:
Given :-
A bag contain 100 cards
To Find :-
Probability of
(i) a number less than 30 (ii) a prime number less than 19
(iii) a prime number greater than 83
(iv) a number which is square of some natural number
Solution :-
1]
There are 29 number between 1 to 30
=> P = 29/100
2]
Prime numbers less than 19 = 2,3,5,7,11,13,17,
=> P = 7/100
3]
Prime numbers greater than 83 = 89 and 97
=> P = 2/100
=> P = 1/50
4]
Square number = 1,4,9,16,25,36,49,64,81,100
=> P = 10/100
=> P = 1/10