數學題不懂 ,求救 !

1. The possible value(s) of X is answer (d). The reason is there can have either no (zero), one, two, three, four or five students wearing blue shirt. Therefore the answer is 0, 1, 2, 3, 4 and 5.

2. The probablity of exactly having two students wearing Blue T-shirt in the classroom is = 0.2 x 0.2 x 0.2 x 0.8 x 0.8 x 2C5 = 0.2 x 0.2 x 0.2 x0.8 x0.8 x 10 = 0.0512, so the answer is (b). Please note that 2C5 means combination of 2 in 5, that is = 5 x 4 / 2 = 10

3. The probability of having at most one student wearing red T-shirt in the classroom

2 ways to calculate:-

1st way:
The probability of all 5 students are wearing blue T-shirt = 0.8 x 0.8 x 0.8 x 0.8 x0.8 x 5C5 = 0.8 x 0.8 x 0.8 X 0.8 x 0.8 = 0.32768 (since 5C5 = 1). The probability of at least 1 student wearing red T-shirt = 1 - 0.32768 = 0.67232

2nd way :
The probability of all 5 students are wearing redT shirt = 0.2 x 0.2 x 0.2 x 0.2 x0.2 x 0C5 = 0.2 x 0.2 x 0.2 X 0.2 x 0.2 = 0.00032 (since 0C5 = 1).
The probability of any 4 students are wearing redT shirt = 0.2 x 0.2 x 0.2 x 0.2 x0.8 x 1C5 = 0.2 x 0.2 x 0.2 X 0.2 x 0.8 x 5 = 0.0064 (since 1C5 = 5).
The probability of any 3 students are wearing redT shirt = 0.2 x 0.2 x 0.2 x 0.8 x0.8 x 2C5 = 0.2 x 0.2 x 0.2 X 0.8 x 0.8 x 10 = 0.0512(since 2C5 = 10).
The probability of any 2 students are wearing redT shirt = 0.2 x 0.2 x 0.8 x 0.8 x0.8 x 3C5 = 0.2 x 0.2 x 0.8 X 0.8 x 0.8 x 10 = 0.2048(since 3C5 = 10). The probability of any 1 student is wearing redT shirt = 0.2 x 0.8 x 0.8 x 0.8 x0.8 x 4C5 = 0.2 x 0.8 x 0.8 X 0.8 x 0.8 x 5 = 0.4096 (since 4C5 = 5).
Total = 0.00032 0.0064 0.0512 0.2048 0.4096 = 0.67232 (also get the same result/answer)

However, answer (d) of 0.00672 looks funny. the answer is neither (a) to (d), do you incorrectly writing (d) 0f 0.672 to be 0.00672?

1.x的可能值是0,1,2,3,4,5becausex can=everythings這題不能算到x可能值.
2.由於穿藍衣的學生有80%,紅衣學生只有20%,第2題的答案可能只有a.
3.紅衣學生的機會是a因為紅衣學生有20%,所以機會一定多.
80%x5=4 20%x5=1