Chapter 13.6, Problem 14PPS

To determine

The probability of each outcome if a dart is equal to land at any place on the dartboard and express the obtained probability as a fraction and in percentage.

  

Answer to Problem 14PPS

The probability of each outcome as a fraction and in percentage is given below.

Explanation of Solution

Given:

Figure is given as

  

A dartboard is divided into 20 equal sections.

Concept Used:

A fraction is defined as a ‘part’ of a ‘whole’.

There are three types of fraction:

1. Proper fraction: Fraction in which numerator is smaller than the denominator.
2. Improper fraction: Fraction in which numerator is larger than the denominator.
3. Mixed fraction: Mixed fraction is combination of whole number and proper fraction.

Calculation:

Figure is given as

  

Above figure is divided into 20 equal sections.

Probability as fraction and in percentage is as follows:

  $P\left(20\right)=\frac{1}{20}=5\%$ = unlikely $P$ (Less than $8$ ) $=\frac{7}{20}=35\%$ = not likely

  $P$ (odd) $=\frac{10}{20}=\frac{1}{2}=50\%$ = equally likely $P$ (prime) = $\frac{8}{20}=\frac{2}{5}=40\%$ = not likely

  $P$ (greater than $16$ ) $=\frac{4}{20}=\frac{1}{5}=20\%=$ unlikely $P$ (multiple of $3$ ) $=\frac{6}{20}=\frac{3}{10}=30\%$ =

  $P$ (less than $21$ ) $\frac{20}{20}=1=100\%=$ certain $P$ ( $25$ ) $=\frac{0}{20}=0\%$ =

  $P$ (even) $=\frac{10}{20}=\frac{1}{2}=50\%$ =equally likely $P$ ( $1or2$ ) $=\frac{2}{20}=\frac{1}{10}=10\%$

  $P$ (greater than $20$ ) $=\frac{0}{20}=0=0\%$ =opposite $P$ (greater than $0$ ) $=\frac{20}{20}=1=100\%$

  $P$ ( not $4,5,6$ ) $=\frac{19}{20}=85\%=$ likely $P$ (not a multiple of $2$ ) $=\frac{10}{20}=\frac{1}{2}=50\%$

  $P$ (not $20$ ) $=\frac{19}{20}=95\%=$ likely $P$ (not prime) $=\frac{12}{20}=\frac{3}{5}=60\%$

  $P$ (not odd) $=\frac{10}{20}=\frac{1}{2}=50\%=$ equally likely $P$ (not $25$ ) $=\frac{20}{20}=1\%=100\%$

  $P$ (Composite) $=\frac{11}{22}=55\%=$ likely $P$ (not $1$ ) $=\frac{19}{20}=95\%$

Conclusion:

Hence, the probability of each outcome as a fraction and in percentage is given as calculated above.