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My name is Ann [436]
3 years ago
7

Hello, hope everyone is well, please help on this Drag and Drop question (:

Mathematics
1 answer:
Mashcka [7]3 years ago
4 0
7 × 100
+ 0 × 10
+ 6 × 1
0 x 0.1 1/10
+ 3 × 0.01 1/100
+ 9 × 0.001 1/1000
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Maria looks at the architectural plan of a four-walled room in which the walls meet each other at right angles. The length of on
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Find the probability that in five tosses of a fair die, a 3 will appear (a) twice, (b) at most once, (c) at least two times.
Jobisdone [24]

Answer:

A) 0.1612

B) 0.8031

C) 0.1969

Step-by-step explanation:

For each toss of the die, there are only two possible outcomes. Either it is a 3, or it is not. The probability of getting a 3 on each toss is independent from other tosses. So we use the binomial probability distribution to solve this problem.

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.

In this problem we have that:

Five tosses, so n = 5

The die has 6 values, from 1 to 6. The die is fair, so each outcome is equally as likely. The probability of a 3 appearing in a single throw is p = \frac{1}{6} = 0.167

(a) twice

This is P(X = 2)

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

P(X = 2) = C_{5,2}.(0.167)^{2}.(0.833)^{3} = 0.1612

(b) at most once

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

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

P(X = 0) = C_{5,0}.(0.167)^{0}.(0.833)^{5} = 0.4011

P(X = 1) = C_{5,1}.(0.167)^{1}.(0.833)^{1} = 0.4020

P(X \leq 1) = P(X = 0) + P(X = 1) = 0.4011 + 0.4020 = 0.8031

(c) at least two times.

Either a 3 appears at most once, or it does at least two times. The sum of the probabilities of these events is decimal 1. So

P(X \leq 1) + P(X \geq 2) = 1

We want P(X \geq 2)

So

P(X \geq 2) = 1 - P(X \leq 1) = 1 - 0.8031 = 0.1969

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Betty was charged 15 1/2% interest for the year
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Answer: James was charged with $180 more for the year that Betty

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