The probability that the committee will consist of 1 from each type of monster is 0.1318 and Suppose that the Pokemon refuse to be on the same committee as a the Trolls.So,the probability that this type of committee is formed is 0.5357

Step-by-step explanation:

No. of Trolls = 3

No. of Nazguls =4

No. of Ents = 4

No. of Pokemon = 5

Total Monsters = 16

We are given that A committee of 4 is to be picked to represent the group at the Monster Bash.

(a) Find the probability that the committee will consist of 1 from each type of monster.

So, the probability that the committee will consist of 1 from each type of monster:

= $\frac{^3C_1 \times ^4C_1 \times ^4C_1 \times ^5C_1}{^{16}C_4}$

= $\frac{\frac{3!}{1!(3-1)!} \times \frac{4!}{1!(4-1)!} \times \frac{4!}{1!(4-1)!}\times \frac{5!}{1!(5-1)!}}{\frac{16!}{4!(16-4)!}}$

= $\frac{\frac{3!}{1!(2)!} \times \frac{4!}{1!(3)!} \times \frac{4!}{1!(3)!}\times \frac{5!}{1!(4)!}}{\frac{16!}{4!(12)!}}$

= $0.1318$

b)Suppose that the Pokemon refuse to be on the same committee as a the Trolls.

So, the probability that this type of committee is formed

= $\frac{(^3C_3 \times ^8C_1)+(^3C_2 \times ^8C_2)+(^3C_1 \times ^8C_3)+(^3C_0 \times ^8C_4)+(^5C_4 \times ^8C_0)+(^5C_3 \times ^8C_1)+(^5C_2 \times ^8C_2)+(^5C_1 \times ^8C_3)}{^{16}C_4}$

= $\frac{(\frac{3!}{3!(3-3)!} \times \frac{8!}{1!(8-1)!})+(\frac{3!}{2!(3-2)!} \times\frac{8!}{2!(8-2)!})+(\frac{3!}{1!(3-1)!} \times\frac{8!}{3!(8-3)!})+(\frac{3!}{0!(3-0)!} \times \frac{8!}{4!(8-4)!})+(\frac{5!}{4!(5-4)!} \times \frac{8!}{0!(8-0)!})+(\frac{5!}{3!(5-3)!} \times \frac{8!}{1!(8-1)!})+(\frac{5!}{2!(5-2)!} \times\frac{8!}{2!(8-2)!})+(\frac{5!}{1!(5-1)!} \times \frac{8!}{3!(8-3)!})}{\frac{16!}{4!(16-4)!}}$

= $0.5357$

Hence The probability that the committee will consist of 1 from each type of monster is 0.1318 and Suppose that the Pokemon refuse to be on the same committee as a the Trolls.So,the probability that this type of committee is formed is 0.5357

4 0

3 years ago

In an isosceles triangle, the longest side measures c units. The other sides of the triangle measure a units. Which equation can

Ira Lisetskai [31]

Answer:

2a² = c²

Step-by-step explanation:

Right triangles follow the Pythagorean Theorem, a² + b² = c². The hypotenuse (c) must be the longest of the sides. In the given triangle, both legs measure a units. So, a = b. Therefore, we have a² + a² = c² or 2a² = c².

5 0

4 years ago

Read 2 more answers

Suppose an article reported that 16% of unmarried couples in the United States are mixed racially or ethnically. Consider the po

makkiz [27]

Answer:

39.36% probability that the proportion of couples in the sample who are racially or ethnically mixed will be greater than 0.17.

Step-by-step explanation:

For each couple, there are only two possible outcomes. Either they are mixed racially or ethnically, or they are not. This means that the binomial probability distribution is used to solve this problem.

However, we are working with samples that are considerably big. So i am going to aproximate this binomial distribution to the normal.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

In this problem, we have that:

$n = 100, p = 0.16$

$E(X) = 100*0.16 = 16$

$\sqrt{Var(X)} = \sqrt{100*0.16*0.84} = 3.67$

When n = 100, what is the probability that the proportion of couples in the sample who are racially or ethnically mixed will be greater than 0.17?

This is 1 subtracted by the pvalue of Z when $X = 100*0.17 = 17$ . So:

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{17 - 16}{3.67}$

$Z = 0.27$

$Z = 0.27$ has a pvalue of 0.6064.

So there is a 1-0.6064 = 0.3936 = 39.36% probability that the proportion of couples in the sample who are racially or ethnically mixed will be greater than 0.17.

4 0

3 years ago

If the measure of two angles in a triangle are 60 and 100 degrees, what is the measure of the third angle? a. 20 degrees) b. 50

bonufazy [111]

Answer:

A. 20 degrees

Step-by-step explanation:

All triangles have 180 degrees in total !

using that info,

100+60= 160

180-160 = 20

4 0

3 years ago