Answer:
Question 1 : 0.44
Question 2: 0.853
Explanation:
We should use combinatorics to solve this problem
Combinations
The number of ways to choose a sample of r elements from a set of n distinct objects where order does not matter and replacements are not allowed
The formula for finding the number of ways you can pick r items from a set of n items where duplicates are eliminated is given by the combinations formula:
where the ! stands for the factorial of the number
Let's take simple example to illustrate this
Suppose we have 3 books labeled A, B. C and we are asked to randomly pick 2 books in one shot. There are 3 possible picks:
AB, AC, BC
Note that though there are six possible arrangements of 2 items from a set of 3, we have to eliminate duplicates because AB is the same as BA.
In the above case, r = 2, n = 3 so using the formula we get
Now to the actual problem
There are a total of 18 students in the class
Number of ways of picking 3 students is
So there are 816 possible ways to pick 3 students from 18 students
There are calculators to perform this gruesome task so I will omit the actual steps and just show the result
Let's consider the first question
Out of the 3 students picked 2 are girls. That means the other one is a boy
Number of ways of picking 2 girls out of 10 is C(10, 2)
C(10, 2) = 45
Then we have to consider the lone boy. Number of ways of picking 1 boy out of 8 is
C(8, 1) = 8
Total number of ways of picking 2 girls and 1 boy
= 45 x 8 = 360
Therefore P(2 girls, 1 boy) :
Second question
To find the number of ways that at least 1 boy can appear in the group is the sum of the number of ways 1, 2 or 3 boys can appear in the group.
Rather than do this, let's approach it in a easier fashion
The probability of at least 1 boy appearing in the group is the complement of no boys on the group, i.e. all volunteers are girls
Number of ways of selecting a volunteer group of all 3 girls:
C(10, 3) = 120
P(no boys in group) = P(all 3 girls in group)
Therefore P(at least 1 boy) = 1 - P(no boys)
= 1-0.147
= 0.853
Could you please let me know if correct? This is a tough subject area for me too :)