1) A jar contains 4 red discs, 6 white discs and 5 green discs. Three discs are removed at random from the jar, one after the other. Once a disc has been removed it is not replaced in the jar.

a) Find the probability that

(i) The first disc is red,

(ii) The second disc is white if the first disc is green.

b) Calculate the probability that

(i) Exactly two of the three discs are red,

(ii) The three discs are the same colour.

a) i ) 4/15

ii) 5/15 * 6/14 = 1/7

b) i) 4/15 * 3/14 = 2/35

ii)6/15 * 4/14 = 4/35

5/15 * 4/14 = 2/21

2/35 + 4/35 + 2/21 = 4/15

ii) red = 4/15 * 3/14 * 2/13 = 4/455

white = 6/15 * 5/14 * 4/13 = 4/91

green = 5/15 * 4/14 * 3/13 = =2/91

4/455 + 2/91 + 4/91 = 34/355

2) Two letters are posted on the same day. Letter A is sent by first-class post and has a probability of 0.9 of being delivered the next day. Letter B is sent by second-class post and has a probability of only 0.3 of being delivered by the next day.

a) Find the probability that

(i) both letters are delivered the next day

(ii) neither letter is delivered the next day

(iii) at least one of the letters is delivered the next day.

b) Given that at least one of the letters is delivered the next day, find the probability that letter A is delivered the next day.

i need to know if i've done these right, and if not then how do i get the correct answer? thanks

i have worked out:

a) i) 0.09 * 0.03 = 0.027

ii) 1 - 0.027 = 0.973

iii) 0.9 + 0.03 = 0.93

b) P( A | B ) = P (both) / P (A)

0.93 = 0.027 / P (A)

P(A) = 0.027/0.93 = 0.29..

3) Shahid, Tracy and Dwight are friends who all have birthdays during January. Assuming that each friend’s birthday is equally likely to be on any of the 31 days of January, find the probability that

a) Shahid’s birthday is on January 3rd

b) both Shahid’s and Tracy’s birthdays are on January 3rd

c) all three friends’ birthdays are on the same day

d) all three friends’ birthdays are on different days.

The answers i have worked out are as follows, but i'm not sure if they are right. could someone check, and if they aren't, could you please tell me how to do them? thank you

a) 1/3

b) 1/3 * 1/3 = 1/9

c) 1/3 * 1/3 * 1/3 = 1/27

d) 1 - 1/27 = 26/27

Thank you and sorry for the very long post