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3 years ago

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Professor Rosencrantz flips a fair coin twice. Professor Guildenstern flips a fair coin thrice. What is the probability that Pro

fessor Rosencrantz obtains more heads than Professor Guildenstern

1 answer:

olasank [31]3 years ago

6 0

Djdkdkjddkdkkddkdkkddjdkdkkdkdkdkdkddkkdkd

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A company is producing two types of ski goggles. Thirty percent of the production is of type A, and the rest is of type B. Five

exis [7]

Answer:

$\dfrac{14}{29}$

Step-by-step explanation:

Let <em>P(A) </em>be the probability that goggle of type A is manufactured

<em>P(B) </em>be the probability that goggle of type B is manufactured

<em>P(E)</em> be the probability that a goggle is returned within 10 days of its purchase.

According to the question,

<em>P(A)</em> = 30%

<em>P(B)</em> = 70%

<em>P(E/A)</em> is the probability that a goggle is returned within 10 days of its purchase given that it was of type A.

P(E/B) is the probability that a goggle is returned within 10 days of its purchase given that it was of type B.

$P(A \cap E)$ will be the probability that a goggle is of type A and is returned within 10 days of its purchase.

$P(B \cap E)$ will be the probability that a goggle is of type B and is returned within 10 days of its purchase.

$P(E \cap A) = P(A) \times P(E/A)$

$P(E \cap A) = \dfrac{30}{100} \times \dfrac{5}{100}\\\Rightarrow P(E \cap A) = 1.5 \%$

$P(E \cap B) = P(B) \times P(E/B)$

$P(E \cap B) = \dfrac{70}{100} \times \dfrac{2}{100}\\\Rightarrow P(E \cap B) = 1.4 \%$

$P(E) = 1.5 \% + 1.4 \% \\P(E) = 2.9\%$

If a goggle is returned within 10 days of its purchase, probability that it was of type B:

$P(B/E) = \dfrac{P(E \cap B)}{P(E)}$

$\Rightarrow \dfrac{1.4 \%}{2.9\%}\\\Rightarrow \dfrac{14}{29}$

So, the required probability is $\dfrac{14}{29}.$

7 0

3 years ago

In July, a paleontologist found 368 fossils at a dig. In August, she found about 14 fossils per day.

Gemiola [76]

Answer: Yes

Step-by-step explanation:

The ratios of number found to the number of days are all equal to 14 fossils per day.

(Plus I just did this and got it wrong but saw the right answer which is this)

3 0

3 years ago

What are all the possible rational roots of f(0) = 2x^4+ x^3+ 4?

ElenaW [278]

Answer: the answer is 4, just 4

7 0

3 years ago

Fill in the blank with the correct response.<br><br> 11 ft = ____in.

Svetllana [295]

Answer:

132 inches

Step-by-step explanation:

We need to multiply both units together; there are 12 inches in a foot and 11 feet. Therefore:

11x12=132

132 inches

5 0

3 years ago

Read 2 more answers

A certain company employs 6 senior officers and 4 junior officers. If a committee is to be created that is made up of 3 senior o

Zigmanuir [339]

Answer:

80

Step-by-step explanation:

A certain company employs 6 senior officers and 4 junior officers. If a committee is to be created that is made up of 3 sr officers and 1 jr officer, how many different committees are possible?

8

24

58

80*

210

I initially got this one wrong, but after I saw the answer which is 80, I was able to solve it. But im not sure if this is the proper way of solving it, or if someone can suggest a more efficient way of solving it?

This is what I did, which was wrong:

Sr Officers + Jr Officers

(6!/3! 3! = 20) + (4!/3! = 4) = 24

It seems like the correct answer is:

Sr Officers X Jr Officers

(6!/3! 3! = 20) x (4!/3! = 4) = 80

If this is the most efficient way of solving, when do you know when to add them as opposed to multiplying them in this case?

7 0

2 years ago