A teacher conducted a fun activity in the class. She put cards numbered from 9 to 90 in a box. Then she called students one by one,from the teams formed by her.The child speaks out any property related to numbers.If he gets a number satisfied that property,the team scored marks otherwise not.
(i) Vanshika speaks out 'divisible by 6'.The probability that her team get marks is
(a)1/6 (b)7/41 (c)7/45 (d)5/27
(ii) Sam speaks out 'a perfect square number'.The Probability of his team getting marks is
(a)7/82 (b)8/82 (c)10/82 (d)7/90
(iii) Preeti says 'a prime number'.The probably of her team getting marks is
(a)19/82 (b)11/41 (c)10/41 (d)21/82
(iv) Karan says 'an odd number'.The probability of getting score in this cases is
(a)20/41 (b)1/2 (c)1/4 (d)1/3
(v) Which of the following property will have maximum chances of getting marks?
(a)an even prime number (b)an even number
(c)a one digit number (d)a two-digit number
Answers
Answer:
total outcome=90
favourable outcome=let x
Given:
A set of cards numbered from 9 to 90 and are put into a box.
Every card is picked and a clue is given about the picked card.
To Find:
1. Probability of student's team getting correct if the drawn card is divisible by 6.
2. Probability of student's team getting correct if the drawn card is a perfect square number.
3. Probability of student's team getting correct if the drawn card is a prime number.
4. Probability of student's team getting correct if the drawn card is an odd number.
5. Probability of higher chance of mentioned categories.
Solutions:
1. Probability of an event is defined as the favorable outcomes divided by the total number of outcomes.
P(Event happening) = (Number of events favoring)/(Total number of events)
Question (i)- OPTION B:
- Probability of the team answer for getting marks if the picked number is divisible by 6:
- Favorable outcomes are : ( 12,18,24,30,36,42,48,54,60,66,72,78,84,90)
- Total number of Outcomes are 82. ( 9 to 90 both inclusive)
=>Probability of getting right :
(Total numbers which are divisible by 6)/(total number of outcomes)
=> P(getting right) = 14/82 ,
=> P(getting right) = 7/41.
Therefore, the probability of the student's team getting the correct answer is 7/41.
Question (ii) - Option A:
- Probability of the team getting correct if the picked card is a perfect square number:
- Total favorable outcomes:(9,16,25,36,49,64,81) (7 favorable outcomes)
- Total number of outcomes is 82.
=>Probability of the student's team to get right:
(Total numbers which are perfect squares)/(Total number of outcomes)
=> Probability of student's team to get right = 7/82.
Therefore, the probability that the student's team will get marks for this case is 7/82.
Question (iii) - Option c:
- Probability of the team getting marks if the picked card is a prime number:
- Total favorable outcomes: (11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89)
- Total number of outcomes is 82.
=> Probability for getting marks: ( Total favorable cases/ Total number of cases)
=> Probability of getting marks = 20/82= 10/41.
Therefore, the probability for the student's team to get a score, in this case, is 10/41.
Question (iv) - Option b:
- Probability for the student's team to get a score if the picked card is an odd number:
- Total favorable outcomes are: (odd numbers between 9 and 90 i.e 50 outcomes).
- Total possible outcomes = 82.
=> Probability of getting right = (Favorable outcomes / Total number of Outcomes)
=> Probability of getting right = 41/82 = 1/2.
Therefore, The probability for the student's team to get score in this case is 1/2.
Question (v) - Option d:
a. There are no even prime numbers after 9 and below 90, Therefore the favorable outcomes are 0. Hence the probability, in this case, is 0.
b. There are a total of 41 even numbers between 9 and 90, Therefore favorable outcomes are 41.
- P(an even number) = 41/82 = 1/2.
c. There is only one single-digit number from 9 to 90, Therefore favorable outcomes are 1.
- P(single digit number) = 1/82.
d. There are 81 two-digit numbers from 9 and 90, Therefore favorable outcomes are 81.
- P(getting a two-digit number) = 81/82.
Therefore, Option d has the highest Probability, Hence it has the highest chance of getting.