A jury is about to be selected from a group of 14 men and 18 women. Use this information to solve every problem on this review.
1. How many ways can a jury of 5 individuals be selected
2. Marks: 1 How many ways can a jury of 5 individuals be selected so that there is exactly 3 women on the jury
3.How many ways can a jury of 5 be selected so that all 5 individuals are males
4.If a jury of 5 is selected, find the probability that there are exactly 4 women on the jury. Type your answer as a decimal rounded to 4 places.
5.If a jury of 5 is selected, find the probability that the jury is made up of all women. Type your answer as a decimal rounded to four places.
6.Let's say that we need to select a jury of 10 individuals. What is the probability that there are an equal number of males and females on the jury? Type your answer as a decimal rounded to four places
Please help me with this questions. ive been trying to do these for the last two days and everytime I do it, its wrong everytime.
1. How many ways can a jury of 5 individuals be selected
2. Marks: 1 How many ways can a jury of 5 individuals be selected so that there is exactly 3 women on the jury
3.How many ways can a jury of 5 be selected so that all 5 individuals are males
4.If a jury of 5 is selected, find the probability that there are exactly 4 women on the jury. Type your answer as a decimal rounded to 4 places.
5.If a jury of 5 is selected, find the probability that the jury is made up of all women. Type your answer as a decimal rounded to four places.
6.Let's say that we need to select a jury of 10 individuals. What is the probability that there are an equal number of males and females on the jury? Type your answer as a decimal rounded to four places
Please help me with this questions. ive been trying to do these for the last two days and everytime I do it, its wrong everytime.
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It is not stats. It is permutations and combinations theory.
You have 32 people, 14 men and 18 women.
1). A jury of 5 means selecting 5 out of 32, which can be done in 32C5 ways.
So there are 32C5 possible juries.
This is (32 x 31 x 30 x 29 x 28) / (5 x 4 x 3 x 2 x 1)
= 8 x 31 x 29 x 28
= 201,376
2) Choose the 3 women first, from 18, giving 18C3
This leaves 2 men out of 14.
Answer = 18C3 x 14C2 = 816 x 91
= 74,256
3) 14C5. Calculate this yourself
4) The number of 4-women juries is 18C4 x 14 (since there are 14 men and only one left to choose).
18C4 = 3060. Multiply this by 14, then divide by the total number of juries possible.
This latter figure is already known: 201,376.
So the required probability is 3060 x 14 / 201376
= 0.2128 to 4 decimal places.
5) No. of juries containing all women is 18C5. This is 8568.
Answer = 8568 / 201376
= 0.04254
6). Number of ways of choosing a jury of 10 is 32C10 (i.e. 10 out of 32)
Number of ways of getting 5 females and 5 males is 14C5 x 18C5 (5 from each group).
So the required probability is 14C5 x 18C5 / 32C10.
I will let you calculate this. I presume you know how to work out the three numbers.
32C10 might take a while to figure.
You have 32 people, 14 men and 18 women.
1). A jury of 5 means selecting 5 out of 32, which can be done in 32C5 ways.
So there are 32C5 possible juries.
This is (32 x 31 x 30 x 29 x 28) / (5 x 4 x 3 x 2 x 1)
= 8 x 31 x 29 x 28
= 201,376
2) Choose the 3 women first, from 18, giving 18C3
This leaves 2 men out of 14.
Answer = 18C3 x 14C2 = 816 x 91
= 74,256
3) 14C5. Calculate this yourself
4) The number of 4-women juries is 18C4 x 14 (since there are 14 men and only one left to choose).
18C4 = 3060. Multiply this by 14, then divide by the total number of juries possible.
This latter figure is already known: 201,376.
So the required probability is 3060 x 14 / 201376
= 0.2128 to 4 decimal places.
5) No. of juries containing all women is 18C5. This is 8568.
Answer = 8568 / 201376
= 0.04254
6). Number of ways of choosing a jury of 10 is 32C10 (i.e. 10 out of 32)
Number of ways of getting 5 females and 5 males is 14C5 x 18C5 (5 from each group).
So the required probability is 14C5 x 18C5 / 32C10.
I will let you calculate this. I presume you know how to work out the three numbers.
32C10 might take a while to figure.
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1) 32C5 = 201376
2) 14C2 * 18C3 = 74256
3) 14C5 = 2002
4) (14C1 * 18C4) / 32C5 = 0.21273637374860956618464961067853
.2127
5) 18C5 / 32C5 = 0.04254727474972191323692992213571
.0425
6) (14C5 * 18C5) / 32C10 = 0.2658896358272476664893359771727
.2659
2) 14C2 * 18C3 = 74256
3) 14C5 = 2002
4) (14C1 * 18C4) / 32C5 = 0.21273637374860956618464961067853
.2127
5) 18C5 / 32C5 = 0.04254727474972191323692992213571
.0425
6) (14C5 * 18C5) / 32C10 = 0.2658896358272476664893359771727
.2659