f.3 maths (probability)

[匿名]

2011-11-22 6:15 am

please show all steps of the following questions please .I wanna know them. Thx soo much.

1.Leo uses 3 cards numbered '7','8','9' to form a 3-digit number at random.
find the expected value of the no.

2.Annie, billy , carol play the game" paper,scissors,rock.'
find the probaility of having a draw,
& find the probability that Annie is the only winner.

3.There are 20$2- and $5 coins in a wallet. Wallace randomly takes a coin from the wallet with an expected value of $3.95.
a) Find the probability of taking a $2-coin
b) If there are 80 coins in total, find the expected value of these coins.

4. Some of the fish in a pond are poisonous. A scientist removes 20 fish from the pond at random and discovers that 8 of them are poisonous.

a) the scientist removes another fish at random from the pond. What is the experimental probability that this fish is poisonous?

b)The scientist brings all 21 fish home and puts them into a tank of water. the scientist's wife takes a fish at random from the tank to cook. What is the theoretical probability that the fish is poisonous if the fish in a) is poisonous?

5. the following no. shows the result of throwing a die 150 times.

no. 12 3 4 5 6
freq. 25 30 20 24 18 x

Which no. is the most favourable outcome? WHy?

ANS
1. 888
2.1/3,1/9
3a).7/20 b)$316
4a)2/5 b)3/7
5. 6

THX^^

回答 (1)

匿名

2011-11-22 1:48 pm

✔ 最佳答案

1. Total number of outcomes = 3P3 = 6
All possible outcomes = {789, 798, 879, 897, 978, 987}

Expected value = (789+798+879+897+978+987)/6
= 5328/6
= 888

2. P(having a draw) = P(all papers)+P(all scissors)+P(all rocks)+P(paper scissors rock)
= (1/3)^3+(1/3)^3+(1/3)^3+(3P3)*(1/3)^3
= 9/27
= 1/3

Note: 3P3 above is the total number of ways 3 people choose 3 different events

P(Annie wins only) = P(Annie paper and other 2 rocks)+P(Annie scissors and other 2 papers)+P(Annie rock and other 2 scissors)
= (1/3)^3+(1/3)^3+(1/3)^3
= 3/27
= 1/9

3a) let x be the number of $2 coins and 20-x be the number of $5 coins
[2x+5*(20-x)]/20 = 3.95
2x+100-5x = 79
3x = 21
x = 7
There are 7 $2 coins.

P(taking a $2 coin) = 7/20

b) number of $2 coins = 80*7/20 = 28
number of $5 coins = 80-28 = 52
value = 2*28+5*52 = 316

Note: the answer below is finding the value of coins instead of the expected value.

4a) P(poisonous fish) = 8/20 = 2/5

b) number of poisonous fish = 21*2/5 = 8.4 (~9)
P(poisonous fish) = 9/21 = 3/7

5. First, find x
x = 150-25-30-20-24-18
x = 33

Number 6 has the largest frequency, so it is the most favorable outcome.

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