Question

O COUNTING AND PROBABILITY

Answer 1

Answer:

a. $Odds = \frac{3}{7}$

b. $Odds = \frac{7}{3}$

Step-by-step explanation:

Given

$n(Black) = 7$

$n(Grey) = 2$

$n(White) = 1$

$n(Total) = 10$

Solving (a): Odds against winning

Since, the arrow must stop at black, then

The odds against winning is calculated as thus:

$Odds = \frac{n(Total) - n(Black)}{n(Black)}$

$Odds = \frac{10 - 7}{7}$

$Odds = \frac{3}{7}$

Solving (b): Odds in favor of winning

Since, the arrow must stop at black, then

The odds is calculated as thus:

$Odds = \frac{n(Black)}{n(Total) - n(Black)}$

$Odds = \frac{7}{10 - 7}$

$Odds = \frac{7}{3}$