hi, i was doing some past paper question on probabilities and need some checking and correction(if needed ) for my answers.
Thanks in advance.

Q1
(a) two clerks A and B work in an office. Thr probability that clerk A will be late on a given day is 0.15,while the prob that clerk B will be late is 0.1.
the prob that both will be late is 0.08

(i)The prob that either or both wll be late on a given day
P(A or B) = 0.15 + 0.1 - 0.08
= 0.17

(ii) Only one clerk comes late on a given day.
0.17 - 0.08 = 0.09


Q2 An experiment consists of rolling a pair of fair dice, Find the prob of rolling a sum of 8 in such an experiment.
P(A) = s/n = 5/6.6 = 5/36

Q3.The prob that a boy in a class is in the football team is 0.4, and the prob that he is in chess team is 0.5,.The prob that a boy in class in both team is 0.2.

(i)Find the prob that a boy chosen at random is in the football team or chess team.
P(A or B ) = 0.4 + 0.5 - 0.2
=0.7

(ii)the prob that the boy is neither in football nor chess team
1 - 0.7
P(A)= 0.3


Q4. The maths students of a sixth form college want to elect a committe of 4 members. In all there are 14 candidates, 6 from 1st year, 8 from second year.

(i)In how many ways can this committe be selected from all candidates
14 = 1001ways
4


(ii) find the number of ways in which only 2nd year students are elected.

8 = 70 ways
4

(iii) find the prob that the committe only consists of 2dn year students
P(A) = s/n
70/1001 = 10/143

(iv) deduce the prob that the committe does not contain any 2nd year students.

P(A) = 1 - 10/143


thanks