Answer:
P(Y=1|X=3)=0.125
Step-by-step explanation:
Given :
p(1,1)=0
p(2,1)=0.1
p(3,1)=0.05
p(1,2)=0.05
p(2,2)=0.3
p(3,2)=0.1
p(1,3)=0.05
p(2,3)=0.1
p(3,3)=0.25
Now we are supposed to find the conditional mass function of Y given X=3 : P(Y=1|X=3)
P(X=3) = P(X=3,Y=1)+P(X=3,Y=2) +P(X=3,Y=3)
P(X=3)=p(3,1) +p(3,2) +p(3,3)
P(X=3)=0.05+0.1+0.25=0.4
Hence P(Y=1|X=3)=0.125
Answer:
Step-by-step explanation:
At the beginning, the jar contains the following beans:
5 purple
6 yellow
8 green
5 orange
Therefore, the total number of jellybeans in the jar tha beginning is:
The number of yellow beans at the beginning is
Therefore, the of selecting a yellow jellybean at the beginning is
After selecting this yellow bean, the yellow bean it is replaced in the jar, so the number of total beans is still n = 24.
And the number of purple beans inside is
So, the probability of selecting a purple bean at the 2nd attempt is
Therefore, the combined probability of selecting a yellow jellybean followed by a purple one is