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sammy [17]
2 years ago
5

A group of 3 explorers travelled through the new Guinea rain forests with 3 Marind-Anim guides. Their inflatable dinghy could on

ly take 2 people at a time and only one of the explorers and one guide could successfully operate it. Once the explorers realised that the Marind-Anim were renowned head hunters they were not willing to ever be outnumbered by them. In spite of these difficulties they worked out a way to negotiate each river. What is the smallest number of crossings needed to get the party safely across a river?
Mathematics
1 answer:
Lesechka [4]2 years ago
4 0

Answer:

Hello,

Step-by-step explanation:

Let's assume A,B,C the 3 explorers and X,Y,Z the 3 guides.

Only A and X can operate the boat.

\begin{array}{|c|c|c|}border\ 1 &boat&border\ 2\\ABCXYZ&-&-\\BCYZ&AX&-\\BCYZ&A&X\\BCY&AZ&X\\BCY&A&XZ\\CY&AB&XZ\\CY&X&ABZ\\Y&CX&ABZ\\Y&X&ABCZ\\-&XY&ABCZ\\-&-&ABCXYZ\\\end{array}

I hope you will understand the travels

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2 years ago
In Illinois, 9% of all drivers arrested for DUI (Driving Under the Influence) are repeat offenders; that is, they have been arre
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Answer:

a) 21.58% probability that exactly 3 people are repeat offenders

b) 97.91% probability that at least one person is a repeat offender

c) 3.69

d) 1.83

Step-by-step explanation:

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

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)}

9% of all drivers arrested for DUI (Driving Under the Influence) are repeat offenders

This means that p = 0.09

41 people arrested for DUI in Illinois are selected at random.

This means that n = 41

a. What is the probability that exactly 3 people are repeat offenders?

This is P(X = 3).

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 3) = C_{41,3}.(0.09)^{3}.(0.91)^{38} = 0.2158

21.58% probability that exactly 3 people are repeat offenders

b. What is the probability that at least one person is a repeat offender?

Either none are repeat offenders, or at least one is. The sum of the probabilities of these outcomes is 1. So

P(X = 0) + P(X \geq 1) = 1

We want P(X \geq 1).

Then

P(X \geq 1) = 1 - P(X = 0)

In which

P(X = 0) = C_{41,0}.(0.09)^{0}.(0.91)^{41} = 0.0209

P(X \geq 1) = 1 - P(X = 0) = 1 - 0.0209 = 0.9791

97.91% probability that at least one person is a repeat offender

c. What is the mean number of repeat offenders?

E(X) = np = 41*0.09 = 3.69

d. What is the standard deviation of the number of repeat offenders?

\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{41*0.09*0.91} = 1.83

4 0
2 years ago
PLEASE HELP!!
allsm [11]

Answer:

im guessing?

Step-by-step explanation:

each=4921

3 0
3 years ago
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