QUESTION 9
Easy
A game of chance consists of spinning an arrow(see fig) which comes to rest pointing at one of the numbers 1, 2, 3, 4, 5, 6, 7, 8, and these are equally likely outcomes. What is the probability that it will point at
(i) 8?
(ii) An odd number?
(iii) A number greater than 2?
(iv) A number less than 9?
(v) A multiple of 3?
SOLUTION
1
Write the sample space
The spinner can point to the numbers 1, 2, 3, 4, 5, 6, 7, 8
So sample space, \(S = \{1, 2, 3, 4, 5, 6, 7, 8\}\)
Total outcomes, \(n(S) = 8\)
So sample space, \(S = \{1, 2, 3, 4, 5, 6, 7, 8\}\)
Total outcomes, \(n(S) = 8\)
2
(i) Probability of getting 8
\(E = \{8\}\)
Number of favourable outcomes, \(n(E) = 1\)
So, \(P(E) = \frac{Favourable\,outcomes}{Total\,outcomes} = \frac{1}{8}\)
The probability of getting an 8 is \(\frac{1}{8}\).
Number of favourable outcomes, \(n(E) = 1\)
So, \(P(E) = \frac{Favourable\,outcomes}{Total\,outcomes} = \frac{1}{8}\)
The probability of getting an 8 is \(\frac{1}{8}\).
3
(ii) Probability of getting an odd number
Odd numbers in the sample space, \(E = \{1, 3, 5, 7\}\)
Number of favourable outcomes, \(n(E) = 4\)
So, \(P(E) = \frac{4}{8} = \frac{1}{2}\)
The probability of getting an odd number is \(\frac{1}{2}\).
Number of favourable outcomes, \(n(E) = 4\)
So, \(P(E) = \frac{4}{8} = \frac{1}{2}\)
The probability of getting an odd number is \(\frac{1}{2}\).
4
(iii) Probability of getting a number greater than 2
Numbers greater than 2, \(E = \{3, 4, 5, 6, 7, 8\}\)
Number of favourable outcomes, \(n(E) = 6\)
\(P(E) = \frac{6}{8} = \frac{3}{4}\)
The probability of getting a number greater than 2 is \(\frac{3}{4}\).
Number of favourable outcomes, \(n(E) = 6\)
\(P(E) = \frac{6}{8} = \frac{3}{4}\)
The probability of getting a number greater than 2 is \(\frac{3}{4}\).
5
(iv) Probability of getting a number less than 9
All numbers in the sample space less than 9, \(E = \{1, 2, 3, 4, 5, 6, 7, 8\}\)
Number of favourable outcomes, \(n(S) = 8\)
So, P(E) = \frac{8}{8} = 1\)
The probability of getting a number less than 9 is 1.
Number of favourable outcomes, \(n(S) = 8\)
So, P(E) = \frac{8}{8} = 1\)
The probability of getting a number less than 9 is 1.
6
(v) Probability of getting a multiple of 3
Multiples of 3, \(E = \{3,6\}\)
Number of favourable outcomes, \(n(E) = 2\)
Sp, \(P(E) = \frac{2}{8} = \frac{1}{4}\)
The probability of getting a multiple of 3 is \(\frac{1}{4}\)
Number of favourable outcomes, \(n(E) = 2\)
Sp, \(P(E) = \frac{2}{8} = \frac{1}{4}\)
The probability of getting a multiple of 3 is \(\frac{1}{4}\)
🏆
Final Answer :
(i) P(getting an 8) = \(\frac{1}{8}\)
(ii) P(getting an odd number) = \(\frac{1}{2}\)
(III) P(number greater than 2) = \(\frac{3}{4}\)
(iv) P(number less than 9) = 1
(v) P(multiple of 3) = \(\frac{1}{4}\)
Concept Note
The sample space is the set of all possible outcomes. An event is the set of outcomes required.
Probability always lies between 0 and 1. 0 means an impossible event and 1 means a certain event.