急! F5 Probability 05x4

12.
(a)
Method 1 :
Number of total combinations
= C(6,2)
= 6!/2!4!
= 15

There are 3 pairs of shoes of the same style.
Hence, the required probability
= 3/15
= 1/5

Method 2 :
Probability of getting a shoe from the cabinet = 1

5 shoes are left in the cabinet. Among them, only 1 shoe is of the same stylewith the first shoe got.
Hence, the required probability
= 1/5

(b)
The required probability
= 1 - (1/5)
= 4/5


20.
(a)
Two-digit numbers : 10, 11, 12, ..., 99
Number of two-digit numbers = 99 - 10 + 1 = 90

Two-digit numbers smaller than 40 : 10, 11, 12, ... 39
Number of two-digit numbers smaller than 40 = 39 - 10 + 1 = 30

The required probability
= 30/90
= 1/3

(b)
Two-digit numbers being a multiple of 10 : 10, 20, 30, ...., 90
Number of two-digit numbers being a multiple of 10 = 9

The required probability
= 9/90
= 1/10

(c)
Repeatedly counted two-digit numbers : 10, 20, 30
Number of repeatedly counted two-digit numbers = 3

The required probability
= (30 + 9 - 3)/90
= 36/90
= 2/5


22.
In the first bag of 12 oranges, 4 are brand A.
In the second bag of 16 oranges, 6 are brand A.

P(both two oranges are NOT brand A)
= P(orange from 1st bag is NOT brand A) x P(orange from 2nd bag is NOT brand A)
= [(12-4)/12] x [(16-6)/16]
= (2/3) x (5/8)
= 5/12

P(at least one of the oranges is brand A)
= 1 - P(both two oranges are NOT brand A)
= 1 - (5/12)
= 7/12