# F.5 Maths ”Probability 2

Q1..

Two fair dice are thrown.

Given that the sum of the two nunbers that show up is greater than 8, find the probability that the two numbers are the same.

Q2..

In the final exam, 30% of the 5B students fail in PHY,20% fails in MATHS,

and 15% fails in both subjects. A student is chosen at random.

a) If the students fails in PHY ,find the probability that he fails in MATHS as well.

b)

If the students fails in MATHS ,find the probability that he fails in PHY as well.

c)Find the probability that he fails in MATHS or PHY.

Update:

Q1 ans::::1/5

Q2a ans:::1/2

Q2b ans:::3/4

Q2c ans:::7/20

Update 2:

Bag X contains 5 black balls,4 white balls, 3green balls.

Bag Y contains 4 black balls,3 white balls.

A ball is chosen at random from bag X and put in to bagY,and then a ball is drawn from bag Y.

Find the probability that the second ball is

Update 3:

a) in bag Y originally and it is black

b) in bad Y originally, given that it is black

Rating

To answer both questions, u hv to understand the concept of conditional prob., i.e., P(A|B) = P(A and B) / P(B).

Q1. finding P(two nos are same | sum of 2 nos &gt; 8)

= P( two nos are same AND sum of 2 nos &gt; 8) / P( sum of 2 nos &gt; 8).

There are 36 combinations in the dice : 1,1 1,2 1,3...... 6,6.

P( two nos are same and sum of 2 nos &gt; 8) = P(5,5 , 6,6) = 2/36

P(sum of 2 nos &gt;8) = P(3,6 4,6, ... 6,6) = 10/ 36

Hence, P(two nos are same | sum of 2 nos &gt; 8) = 2/36/ 10/36 = 1/5

Q2 P(fail in Phy) =.3, P(fail in Math) =.2, P (fail in Phy and fail in Math)=

0.15

a) P(fail in Math | fail in Phy) = P(fail in Math and Phy) / P(fail in Phy)

= 0.15 / 0.3 = 1/2

b) P(fail in Phy | fail in Math) = P(fail in Phy and Math) / P(fail in Math)

= 0.15/ 0.2 = 3/4

c) P( fail in Math or Phy) = P(fail in Math) + P(fail in Phy) - P(fail in Math and Phy) = 0.2 + 0.3 - 0.15 = 7/20

Q1. 1/6*1/6 +1/6*1/6 = 2/36 = 1/18

只要5,5 & 6,6 大過8。

diec出現5的機會率是1/6,所以出現5,5 的機會率是1/6*1/6。同樣道理6,6 的機會率就是1/6*1/6。 現在5,5 & 6,6 都可以就將它們的機會率梳加就可以了。

Q.2 a) 50%

一班有30%的人fail phy,15%的人2科都fails! 即是fail phy 中的一半人maths 都fail. 咁即是50%啦~

b) 75%

有同一樣的道理, 20% 的人fail maths,15%的人2科都fails! 即是有75%的人 fail左maths 同時fail phy,所以答案75%!

c) 15%

題目比左答案你了, 15%的人同時fails 2 科!