Math Exercise

[匿名]

2013-02-17 3:18 pm

Help me!

To slove the following the questions

1. An advisory boared consists of 6 members selected from 8 government
officials and 6 legislative councillors. Find the probabilities that
the advisory board includes
a) exactly 4 government officials
b) an equal number of government officials and legislative councillors

2. In a certain district of a city, the probability of a household having an oven
is 0.05 and the probability of having an air-cleaner is 0.12. If a household
is selected at random from the district, find the probabilities that the
household has
a) both appliances
b) only one of the two appliances
c) at least one of the two appliances

3. In a particular mission, the probability that a bomber hits the target is 4/5.
If 4 bombers are prepared to fire. find the probabilities that
a) all the bombers hit the target
b) at least one of the bombers hits the target

4.In a game set for children, there are 7 pieces of triangle, of which 3 are
blue and 4 are red, and 11 pieces of square, of which 5 are blue and 6 are
red. If a child selects 2 pieces at random without replacement. Find the
probabilities that the two pieces are of
a) the same shape
b) the same colour
c) the same shape and colour
d) the same shape given that they are of the same colour

回答 (1)

賣女孩的火柴

2013-02-17 7:14 pm

✔ 最佳答案

1.
(a)
G : a government official
L : a legislative councilor

P(4G 2L)
= 8C4 x 6C2 / 14C6
= (8!/4!4!) x (6!/2!4!) / (14!/6!8!)
= 50/143

(b)
P(3G 3L)
= 8C3 x 6C3 / 14C6
= (8!/3!5!) x (6!/3!3!) / (14!/6!8!)
= 160/429

2.
(a)
O: having oven, O': no oven
A: having air-cleaner, A': no air-cleaner

P(O A)
= 0.05 x 0.12
= 0.006

(b)
P(only 1 appliance)
= P(O A') + P(O' A)
= 0.05 x (1 - 0.12) + (1 - 0.05) x 0.12
= 0.158

(c)
P(at least 1 appliance)
= 1 - P(O' A')
= 1 - (1 - 0.05) x (1 - 0.12)
= 0.164

3.
H : hit the target
H' : miss the target

(a)
P(4H)
= (4/5)⁴
= 256/625

(b)
P(at least 1H)
= 1 - P(4H')
= 1 - [1 - (4/5)]⁴
= 624/625

4.
T: triangle, S:square
B: blue, R: red

7T : 3BT 4RT
11S: 5BS, 6RS
18 pieces: 8B, 10R

(a)
P(same shape)
= P(T T) + P(S S)
= (7/18) x (6/17) + (11/18) x (10/17)
= 76/153

(b)
P(same colour)
= P(B B) + P(R R)
= (8/18) x (7/17) + (10/18) x (9/17)
= 73/153

(c)
P(same shape and same colour)
= P(BT BT) + P(RS RS) + P(BS BS) + P(RS RS)
= (3/18) x (2/17) + (4/18) x (3/17) + (5/18) x (4/17) + (6/18) x (5/17)
= 2/9

(d)
P([same shape] | [same colour])
= P(same shape and same colour) / (same colour)
= (2/9) / (73/153)
= 34/73

參考: 賣女孩的火柴

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