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# 明天考試了，有幾條問題想問大家。幾題中3的數學題..

Q1. There are two concentric circles(同心圓) of radii 12 cm and 2cm respectively.

(a) Find the area of the shaded region on the dartboard.

(b) Two darts are thrown and hit the dartboard.Find the probability that

(i)both darts hit the shaded region

(ii) only one dart hits the shaded region

Q2. There are 8 white socks ,4 yellow socks and 2 red socks in a drawer. A boy randomly takes out 2 socks from the drawer.

(a) Find the probability that the socks taken out are both white

(b) Find the probability that the socks taken out are of the same colour

Q3. Mr Sun is waiting for a bus at a bus stop. It is known that 75% of the buses are air-conditioned, of which 20% have Octopus machines installed. No Octopus machines have been installed on buses without air-conditioning.

(a) Find the probability that the next bus has an Octopus machine installed.

(b) The bus fare is \$3.00. Mr Sun does not have an Octopus card but has 1-dollar coins and three 2-dollar coins in his pocket. If he randomly takes out two coins, what is the probability that the total value of these coins is exactly \$3.00?

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Q1. There are two concentric circles(同心圓) of radii 12 cm and 2cm respectively.

(a) Find the area of the shaded region on the dartboard.

(b) Two darts are thrown and hit the dartboard.Find the probability that

(i)both darts hit the shaded region

(ii) only one dart hits the shaded region

Q2. There are 8 white socks ,4 yellow socks and 2 red socks in a drawer. A boy randomly takes out 2 socks from the drawer.

(a) Find the probability that the socks taken out are both white

8/14 x 7/13 = 4/13

(b) Find the probability that the socks taken out are of the same colour

P(both white) + P(both yellow) + P(both red)

= 8/14 x 7/13 + 4/14 x 3/13 + 2/14 x 1/13

= 70/182 = 5/13

Q3. Mr Sun is waiting for a bus at a bus stop. It is known that 75% of the buses are air-conditioned, of which 20% have Octopus machines installed. No Octopus machines have been installed on buses without air-conditioning.

(a) Find the probability that the next bus has an Octopus machine installed.

P(air-conditioned) x P(octopus)

= 0.75 x 0.2 = 0.15 = 15%

(b) The bus fare is \$3.00. Mr Sun does not have an Octopus card but has 1-dollar coins and three 2-dollar coins in his pocket. If he randomly takes out two coins, what is the probability that the total value of these coins is exactly \$3.00?

你無講有幾多個一蚊，我當係y個。

中次抽兩個銀其實都等於一先一後。

P(1, 2) + P(2, 1)

= y/(y+3) x 3/(y+2) + 3/(y+3) x y/(y+2)

= 6y/((y+3)(y+2))