Given:
[tex]\begin{gathered} Total\text{ number of crayons = 24} \\ Number\text{ of red crayons = 8} \\ Number\text{ of yellow crayons = 7} \\ Number\text{ of blue crayons = 9} \end{gathered}[/tex]Required:
Probability of removal of the crayon as blue, red, and yellow respectively
Explanation:
The probability of removal of the first blue crayon is calculated as,
[tex]\begin{gathered} Probability\text{ = }\frac{^9C_1}{^{24}C_1} \\ Probability\text{ =}\frac{9}{24} \end{gathered}[/tex]The probability of removal of the second red crayon is calculated as,
[tex]\begin{gathered} Probability\text{ = }\frac{^8C_1}{^{24}C_1} \\ Probability\text{ = }\frac{8}{24} \end{gathered}[/tex]The probability of removal of the third yellow crayon is calculated as,
[tex]\begin{gathered} Probability\text{ = }\frac{^7C_1}{^{24}C_1} \\ Probability\text{ = }\frac{7}{24} \end{gathered}[/tex]Therefore the required probability is calculated as,
[tex]\begin{gathered} Required\text{ probability = }\frac{9}{24}\text{ }\times\text{ }\frac{8}{24}\text{ }\times\text{ }\frac{7}{24} \\ Required\text{ probability = }\frac{9\times8\times7}{24\times24\times24} \\ Required\text{ probability = }\frac{504}{13824} \\ Required\text{ probability = 0.0365} \\ \end{gathered}[/tex]Answer:
Thus the required probability is 0.0365
