A die has been \"loaded\" so that the probability of rolling anyeven number is

5

27

and the probability of rolling any odd number is

4

27

. (Assume the die is six-sided with each side numbered onethrough six.)

(a)

Find the following probabilities. Enter your probabilities asfractions.

Pr(2 ∩even)	=
Pr(even)	=
Pr(2 |even)	=

What is the probability of rolling a 2, given that an evennumber is rolled?

(b)

Find the following probabilities. Enter your probabilities asfractions.

Pr(3 ∩(3 or 6))	=
Pr(3or 6)	=
Pr(3 |(3 or 6))	=

What is the probability of rolling a 3, given that a numberdivisible by 3 is rolled?

A bag contains 5 red balls and 7 white balls. Two balls aredrawn without replacement. (Enter your probabilities asfractions.)

(a) What is the probability that the second ball is white, giventhat the first ball is red?


(b) What is the probability that the second ball is red, given thatthe first ball is white?


(c) Answer part (a) if the first ball is replaced before the secondis drawn.

A red ball and 5 white balls are in a box. If two balls aredrawn, without replacement, what is the probability of getting eachof the following? (Enter your probabilities as fractions.)

(a) a red ball on the first draw and a white ball on thesecond


(b) 2 white balls


(c) 2 red balls