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Flashcards: Independence

Two fair dices are rolled. If the first die is an odd number what is the probability that the sum of the two dice equal 8?

$\frac{1}{8}$

$\frac{2}{15}$

$\frac{1}{9}$

$\frac{2}{24}$

$\frac{3}{16}$

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Flashcards: Independence

Two fair dices are rolled. If the first die is an odd number what is the probability that the sum of the two dice equal 8?

Your answer:

$\frac{1}{8}$

Your answer:

$\frac{2}{15}$

Your answer:

$\frac{2}{24}$

Your answer:

$\frac{3}{16}$

Correct answer:

$\frac{1}{9}$

Explanation:

First, recall that each die is rolled independently.

Now, it is known that the first die is an odd number therefore the possible options are:

$\text{Die}_1=1,3,5$

From here, find the number of combinations each one will have to make a sum of 8 with the other die.

$\text{Die}_2=1,2,3,4,5,6$

By investigation, die number one cannot be one because it along with any value from die two will not equal eight.

Therefore, investigate when die one is three.

$\text{Sum}=3+5=8$

Next, if die one is five then the possible sum is,

$\text{Sum}=5+3=8$

Therefore there are a total of two possibilities of rolling a sum equaled to eight.

From here, identify the total number of options the sum could be when it does not equal eight.

$\\\text{Possibilities for Die}_1\times \text{Possibilities for Die}_2 \\=3\times 6 \\=18$

$\text{Probability of Sum of 8}=\frac{\text{Combinations equalling 8}}{\text{Total Possibilities}}$

$\text{Probability of Sum of 8}=\frac{2}{18}=\frac{1}{9}$

Flashcards: Independence

A coin is loaded so that it comes up heads 60% of the time. If it is tossed six times, what is the probability that it will come up heads at least five times?

Choose the closest response.

0.15

0.35

0.2

0.25

0.3

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Flashcards: Independence

A coin is loaded so that it comes up heads 60% of the time. If it is tossed six times, what is the probability that it will come up heads at least five times?

Choose the closest response.

Your answer:

0.15

Your answer:

0.35

Your answer:

0.2

Your answer:

0.3

Correct answer:

0.25

Explanation:

Since each trial can have one of two outcomes, heads or tails, this is an example of a Bernoulli process.

The probability that trials will result in successes in a Bernoulli process is

$C(n, k) p^{k}q^{n-k}$ ,

where is the probability of a success in any given trial and q = 1-p is the probability of a failure.

Since there are six tosses, set n = 6 . We can call heads the success with probability p = 0.6 , and tails the failure with probability q = 1-p = 0.4 . Accordingly, the probability P(k ) that exactly heads will come up is

$P(k) = C(6, k) 0.6^{k}0.4^{6-k}$

Since we are looking for the probability of heads coming up at least five times, evaluate P(5)+P(6) as follows:

$P(5) = C(6, 5) 0.6^{5}0.4^{6-5} = 6 (0.07776) (0.4) = 0.186624$

$P(6) = C(6,6) 0.6^{6}0.4^{6-6} = 1 (0.046656)(1) = 0.046656$

P(5)+P(6) = 0.186624+0.046656 = 0.23328

Of the five choices, 0.25 comes closest.

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Flashcards: Independence

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Flashcards: Independence

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DMCA Complaint

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Complaint Details

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