英文數學工課,今日急要答案,數學高手幫忙

1(i) as only 1 correct answer in 4 options,
required probability = 1/4
(ii) required expected number = (1/4)(20) = 5

2(i) required probability = 5/20 = 1/4
(ii) required probability = (20-5)/20 = 3/4 (OR 1 - 1/4 = 3/4)
required expected value = (1/4)(500)+(3/4)(100) = $200

3(i) as a coin has only two faces(head and tail),
probability of getting tail = 1/2
required probability = (1/2)(1/2)(1/2)(1/2)(1/2) = (1/2)^5 = 1/32
(ii) at least one head = no all tails
required probability = 1 - 1/32 = 31/32

4(i) number of odd numbers from 1 to 20 is 10 (no. 1,3,5,7,9,11,13,15,17,19)
required probability = 10/20 = 1/2
(ii) number of numbers which are divisible by 3 is 6 (no. 3,6,9,12,15,18)
required probability = 6/20 = 3/10
(iii) number of number which are odd and divisible by 3 is 3 (no. 3,9,15)
required probability = 3/20
(OR as probability of odd number = 1/2,
probability that number is divisible by 3 = 3/10
probability of both cases = (1/2)(3/10) = 3/20)
(iv) number of number which are odd or divisible by 3 is 13(10+6-3)
(no. 1,3,5,7,9,11,13,15,17,19,6,12,18)
required probability = 13/20
(OR as probability of odd number = 1/2,
probability that number is divisible by 3 = 3/10
probability of both cases = (1/2)(3/10) = 3/20
probability that number is odd or divisible by 3 = (1/2)+(3/10) - (3/20) = 13/20
ps. the required probability ≠ (1/2)+(3/10) as no. 3,9,15 are counted twice)

5 required expected amount = (1000)(1/800)+(500)(2/800)+(100)(10/800)
= (1000/800)+(1000/800)+(1000/800) = 3(1000/800) = $3.75

6 probability of head in a coin = 1/2,
probability of tail in a coin = 1/2
probability of 2 heads in 2 coins = (1/2)(1/2) = 1/4
probability of only 1 head(1 head and 1 tail) in 2 coins = 1/4 + 1/4 = 1/2
probability of no heads(2 tails) in 2 coins = 1/4
required expected gain = (1/4)(10)+(1/2)(5)+(1/4)(-24) = -$1

question 7 is posted in a supplement.

2014-04-16 17:32:20 補充：
question 7 is posted in area of opinion.

2014-04-16 17:33:28 補充：
7(i) required probability = 6/(6+4) = 3/5
(ii) required probability = 9/(9+3) = 3/4
(iii) required probability = 3/5+3/4-(3/5)(3/4) = 9/10