Hi. economyst. Thanks for your help with my other questions. But I am still stuck with this question:
@@@@My question: Rain is an amazing singer, but cannot play any instruments. He desperately wants a rock band that has a drummer, a guitarist, a bass player, and himself on vocals. He decides to post an ad at the local coffee house for open auditions for his band - The Combinations.
At the auditions, Rain gets 5 females and 9 males trying out for the remaining 3 positions in the band that can play all the instruments.
a) What is the probability that the band will have 3 males and 1 female?
b) What is the probability that the band will have at least 2 males?@@@@
@@@@economyst answered:
* Another Data Management Question - economyst, Saturday, September 26, 2009 at 11:02am
Follow the logic i gave you in your previous post. Remember, the formula for n-choose-x is n!/x!*(n-x)! where ! means factorial.
* Another Data Management Question - economyst, Saturday, September 26, 2009 at 1:43pm
hint for b) Since Rain is male, having at least two males means picking at least one male. Which is equal to (1-P) where P is the probability of picking 3 females.@@@@
I would be really greatful if you help me solve it. Thanks again. :)
Out of the 14 try-outs, he picks 3. The possible combinations are 14-choose-3 = 14!/3!*(14-3)! = (12*13*14)/(1*2*3) = 364
a) to get 3 M and 1 F, besides himself he needs to pick 2 M and 1 F. There are 9-choose-2 possible picks of the males. and 4-choose-1 females. Following the n-choose-x formula:
8*9/2 = 36 possible male picks and
4/1 = 4 female.
So the total possible ways to pick 2 males and 1 female is 36*4=144, The probability is therefore 144/364
b) From my hint, the prob of getting at least 2 Males is (1-P) where P is the probability of getting all female. The number of ways to pick 3 females out of the 4 available is 4-choose-3 = 4!/3!(4-3)! = 4. So P= 4/364.
Of course! I'm here to help you. Let's go through the steps to solve these probability questions.
a) To find the probability that the band will have 3 males and 1 female, we need to calculate the ratio of successful outcomes to total outcomes.
Step 1: Total Outcomes
The total number of ways to choose 3 positions out of the 14 remaining musicians (9 males + 5 females) is calculated using the formula for "n choose x" which is n! / (x! * (n-x)!). In this case, n = 14 (total number of musicians) and x = 3 (number of positions in the band), so the total outcomes would be 14! / (3! * (14-3)!) = 14! / (3! * 11!).
Step 2: Successful Outcomes
Now we need to determine the number of ways to pick 3 males and 1 female out of the available musicians. There are 9 males to choose from, so the number of ways to select 3 males out of the 9 would be 9 choose 3, written as 9! / (3! * (9-3)!).
Similarly, there are 5 females to choose from, so the number of ways to select 1 female out of the 5 would be 5 choose 1, written as 5! / (1! * (5-1)!).
Therefore, the number of successful outcomes would be (9 choose 3) * (5 choose 1).
Step 3: Calculation
To find the probability, we divide the number of successful outcomes by the total outcomes:
Probability = (Number of Successful Outcomes) / (Total Outcomes)
b) To find the probability that the band will have at least 2 males, we will use a complementary approach. First, we find the probability of selecting 3 females, and then subtract this probability from 1 to find the probability of having at least 2 males.
Step 1: Probability of selecting 3 females
We already calculated this probability in part a), which is (Number of Successful Outcomes) / (Total Outcomes).
Step 2: Probability of having at least 2 males
The probability of having at least 2 males is equal to 1 minus the probability of selecting 3 females:
Probability = 1 - Probability of selecting 3 females
Now, I will let you apply the formulas and calculations to find the exact answers for parts a) and b) of the question. If you have any further questions or need assistance in solving any specific steps, feel free to ask.