A game of chance consists of spinning an arrow (see Figure) which comes to rest pointing at one of the numbers Class 9

A game of chance consists of spinning an arrow (see Figure) which comes to rest pointing at one of the numbers Class 9

Question 1.

A game of chance consists of spinning an arrow (see Figure) 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 Class 9

i. 8

ii. An odd number?

iii. A number greater than 2?

iv. A number less than 9?

v. A multiple of 3?

Solution:

i. Sample space S = {1, 2, 3, 4, 5, 6, 7, 8}

Total number of outcomes = 8

Favourable outcome = {8}

Number of favourable outcomes = 1

∴ P(8) = $\frac{\text { Number of favourable outcomes }}{\text { Total number of outcomes }}=\frac{1}{8}=0.125$

ii. Favourable outcomes for odd numbers = {1, 3, 5, 7}

Number of favourable outcomes = 4

∴ P(an odd number)

$=\frac{\text { Number of favourable outcomes }}{\text { Total number of outcomes }}=\frac{4}{8}=\frac{1}{2}=0.5$

iii. Favourable outcomes for numbers greater than 2 = {3, 4, 5, 6, 7, 8}

Number of favourable outcomes = 6

∴ P (a number greater than 2)

$=\frac{\text { Number of favourable outcomes }}{\text { Total number of outcomes }}=\frac{6}{8}=\frac{3}{4}=0.75$

iv. Favourable outcomes for number less than 9 = {1, 2, 3, 4, 5, 6, 7, 8}

Number of favourable outcomes = 8

∴ P(a number less than 9)

$=\frac{\text { Number of favourable outcomes }}{\text { Total number of outcomes }}=\frac{8}{8}=1$

v. Favourable outcomes for multiples of 3: {3, 6}

Number of favourable outcomes = 2

∴ P(multiple of 3)

$=\frac{\text { Number of favourable outcomes }}{\text { Total number of outcomes }}=\frac{2}{8}=\frac{1}{4}=0.25$