3) Consider an urn containing ten balls; one of them with the number 1 on it, tw

Question

3) Consider an urn containing ten balls; one of them with the number 1 on it, two of them with the number 2 on them, three of them with the number 3 on them, and four of them with the number 4 on them. Suppose that a ball will be randomly selected from the ten balls in the urn, and the number on it observed, and then a second ball will be randomly drawn from the nine remaining balls. (a) What is the probability that the number on the 2nd ball will be greater than the number on the first ball? (b) What is the probability that the number on the 1st ball will be a 2, given that the number on the 2nd ball will be greater than the number on the first ball? (c) Letting A be the event that the number on the first ball will be a 1, and B be the event that the number on the 2nd ball will be a 2, are A and B independent events? Answer yes or no, and justify your answer using the definition of two events being independent.

Explanation / Answer

a probability that the number on the 2nd ball will be greater than the number on the first ball

= P(first ball has lowest number and second any of remaing 9 high+first ball has 2nd lowest number and second any of remaing 8 high+...............) =(9+8+7+6+5+4+3+2+1)/90 =1/2

b)probability that the number on the 1st ball will be a 2, given that the number on the 2nd ball will be greater than the number on the first ball =P( numebr on 2nd ball would be any 8 higher number)P(2nd ball has greater number)

=(8/90)/(1/2)=8/45

c)P(A) =1/10

and P(B)=P( 1st ball not 2 and secoind 2) =(9/10)*(1/9)=1/10

also P(AnB)=P( first ball 1 and second 2) =(1/10)*(1/9)=1/90

as P(AnB) is not equal to P(A)*P(B)

therefore not independent.

Related Questions

Navigate

• Browse (All)
• Browse 3
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.