Answer: 0.0309
Step-by-step explanation:
Given: In advanced statistics class, there are 20 Statistics majors, 15 Mathematics majors, 10 Computer Science majors, and 5 Electric Engineering majors.
Total = 20+15+10+5 =50
Number of combinations of selecting r things out of n = [tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex]
The number of ways to choose a sample of 10 put of 50=[tex]^{50}C_{10}=\dfrac{50!}{10!40!}[/tex]
Number of ways to choose 5 Statistics majors, 3 Mathematics majors, 2 Computer Science majors, and 0 Electric Engineering majors = [tex]^{20}C_5\times ^{15}C_3\times ^{10}C_2\times ^5C_0\\\\=\dfrac{20!}{5!15!}\times\dfrac{15!}{3!12!}\times\dfrac{10!}{2!8!}\times\dfrac{5!}{5!0!}[/tex]
Required probability = [tex]\dfrac{\frac{20!}{5!15!}\times\frac{15!}{3!12!}\times\frac{10!}{2!8!}\times\frac{5!}{5!0!}}{\frac{50!}{10!40!}}= 0.0309[/tex]
Hence, the required probability = 0.0309
