Answer: a) [tex]\dfrac{32}{243}[/tex] b) [tex]\dfrac{256}{6561}[/tex] c) [tex]\dfrac{128}{6561}[/tex] d) [tex]\dfrac{6305}{6561}[/tex]
Step-by-step explanation:
Since we have given that
Probability that each person agrees independently to be interviewed = [tex]\dfrac{2}{3}[/tex]
(a) 5 names?
If it has 5 names, then the probability would be
[tex](\dfrac{2}{3})^5\\\\=\dfrac{32}{243}[/tex]
(b) What if it has 8 names?
If it has 8 names, then the probability would be
[tex](\dfrac{2}{3})^8=\dfrac{256}{6561}[/tex]
(c) If the list has 8 names what is the probability that the reviewer will contact exactly 7 people in completing her assignment?
[tex]^8C_7(\dfrac{2}{3})^7(\dfrac{1}{3})\\\\=\dfrac{128}{6561}[/tex]
(d) With 8 names, what is the probability that she will complete the assignment without contacting every name on the list?
[tex]1-P(X=8)\\\\=1-^8C_8(\dfrac{2}{3})^8\\\\=1-\dfrac{256}{6561}\\\\=\dfrac{6561-256}{6561}\\\\=\dfrac{6305}{6561}[/tex]
Hence, a) [tex]\dfrac{32}{243}[/tex] b) [tex]\dfrac{256}{6561}[/tex] c) [tex]\dfrac{128}{6561}[/tex] d) [tex]\dfrac{6305}{6561}[/tex]
