[tex] \\ \large\color{grey}{◈ ━━━━━━━━━━━━ ⸙ ━━━━━━━━━━━━ ◈} [/tex]
[tex]\huge\color{pink}{\mid{\underline{\overline{{{\sf \: \: \: \: \: \: \: \: \: \: \: \: \: ANSWER \: \: \: \: \: \: \: \: \: \: \: \: \: }}}} \mid}}[/tex]
[tex] \large\color{grey}{◈ ━━━━━━━━━━━━ ⸙ ━━━━━━━━━━━━ ◈} \\ [/tex]
1) A box contains 6 red balls numbered 1 to 6 and 8 blue balls numbered 1 to 8. A ball is drawn at random from the box. Find the probability that the ball is: a. red or odd-numbered
[tex] \\ [/tex]
SOLUTION:
P(red or odd-numbered) = [tex]\frac{6+4}{14}[/tex] = [tex]\frac{10}{14}[/tex] = [tex]\frac{5}{7} \\[/tex]
Thus, the probability of getting a red or odd-numbered is [tex]\frac{5}{7}[/tex]
[tex] \large\color{grey}{◈ ━━━━━━━━━━━━ ⸙ ━━━━━━━━━━━━ ◈} \\ [/tex]
2) Refer to #1 b. blue or even-numbered
[tex] \\ [/tex]
SOLUTION:
P(blue or even-numbered) = [tex]\frac{8+3}{14}[/tex] = [tex]\frac{11}{14}[/tex]
Thus, the probability of getting a blue or even-numbered is [tex]\frac{11}{14} \\ [/tex]
[tex] \large\color{grey}{◈ ━━━━━━━━━━━━ ⸙ ━━━━━━━━━━━━ ◈} \\ [/tex]
3) Two cards are drawn at random from a standard deck of 52 cards, without replacement. What is the probability that both cards drawn are queens?
[tex] \\ [/tex]
SOLUTION:
P(QQ) = [tex]\frac{4}{52} \times \frac{3}{51}[/tex] = [tex]\frac{1}{221} \\ [/tex]
Thus, the probability that they will both be queen is [tex]\frac{1}{221}[/tex]
[tex] \large\color{grey}{◈ ━━━━━━━━━━━━ ⸙ ━━━━━━━━━━━━ ◈} \\ [/tex]
4) Mario has 45 red chips, 12 blue chips, and 24 white chips. What is the probability that Mario randomly selects a red chip or a white chip?
[tex] \\ [/tex]
SOLUTION:
P(red or white) = [tex]\frac{45 + 24}{81}[/tex] = [tex]\frac{69}{81}[/tex] = [tex]\frac{23}{27} \\ [/tex]
Thus, the probability that Mario randomly selects a red chip or a white chip is [tex]\frac{23}{27}[/tex]
[tex] \large\color{grey}{◈ ━━━━━━━━━━━━ ⸙ ━━━━━━━━━━━━ ◈} \\ [/tex]
5) Ruby's dog has 8 puppies. The puppies include 2 white females, 3 mixed-color females, 1 white male, and 2 mixed-color males. Ruby wants to keep one puppy. What is the probability that she randomly chooses a puppy that is female and white?
[tex] \\ [/tex]
SOLUTION:
P(female and white) = [tex]\frac{2 + 8}{81}[/tex] = [tex]\frac{1}{4} \\ [/tex]
Thus, the probability that she randomly chooses a puppy that is female and white is [tex]\frac{1}{4} [/tex]
[tex] \large\color{grey}{◈ ━━━━━━━━━━━━ ⸙ ━━━━━━━━━━━━ ◈} \\ [/tex]
6) There are a total of 48 students in Grade 10 Faith. Twenty are boys and 28 are girls. If a teacher randomly selects a student to represent the class in a school meeting, what is the probability that a.) a boy is chosen?
[tex] \\ [/tex]
SOLUTION:
P(boy) = [tex]\frac{20}{48}[/tex] = [tex]\frac{5}{12} \\ [/tex]
Thus, the probability that a boy is chosen is [tex]\frac{5}{12} [/tex]
[tex] \large\color{grey}{◈ ━━━━━━━━━━━━ ⸙ ━━━━━━━━━━━━ ◈} \\ [/tex]
b.) A girl is chosen?
[tex] \\ [/tex]
SOLUTION:
P(female) = [tex]\frac{28}{48}[/tex] = [tex]\frac{7}{12} \\ [/tex]
Thus, the probability that a female is chosen is [tex]\frac{7}{12} [/tex]
[tex] \\ \large\color{grey}{◈ ━━━━━━━━━━━━ ⸙ ━━━━━━━━━━━━ ◈} \\ [/tex]
