# Thread: Discrete Probability Distribution II

1. ## Discrete Probability Distribution II

from walpole 5.61

Suppose the probability is 0.8 that any given person wll believe a tale about the transgressions of a famous actress.

a) the sixth person to hear this tale is the forth one to believe it ?
b) what is the probability that the thrd person to hear this tale is the first one to believe it ?

i know p= 0.80 and q = 1- 0.8=0.20

but how should i apply the above to the questions ?
i don't even know how many people are listening to the tale.
pls explain.

2. Originally Posted by hazel
from walpole 5.61

Suppose the probability is 0.8 that any given person wll believe a tale about the transgressions of a famous actress.

a) the sixth person to hear this tale is the forth one to believe it ?
b) what is the probability that the thrd person to hear this tale is the first one to believe it ?

i know p= 0.80 and q = 1- 0.8=0.20

but how should i apply the above to the questions ?
i don't even know how many people are listening to the tale.
pls explain.
a) is a negative binomial distribution problem.
b) (0.2)(0.2)(0.8) = ....

3. Hello, Hazel!

Suppose the probability is 0.8 that any given person will believe a rumor of a scandal.

a) What is the probability that the 6th person to hear the rumor is the 4th one to believe it ?
Let $B$ = the person believes the rumor.
and $N$ = the person does not believe the rumor.

Among the first 5 who heard the rumor, there were 3 B's (and 2 N's).
. . This probability is: . ${5\choose3}(0.8)^3(0.2)^2$

Then the 6th person is a B: . $0.8$

Therefore: . $P(\text{6th is 4th B}) \:=\:{5\choose3}(0.8)^3(0,2)^2\cdot(0.8) \;=\;0.16384$

b) What is the probability that the 3rd person to hear this rumor is the first to believe it ?

The first two were N's: . $(0.2)^2$

The third is a B: . $0.8$

Therefore: . $P(\text{3rd is 1st B}) \:=\:(0.2)^2(0.8) \;=\;0.032$

4. Originally Posted by Soroban
Hello, Hazel!

Let $B$ = the person believes the rumor.
and $N$ = the person does not believe the rumor.

Among the first 5 who heard the rumor, there were 3 B's (and 2 N's).
. .

refering to the bold comments above, how do you know 3B and 2 N ?
it can also be other combination ?