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Contact [7]
3 years ago
14

A standard deck of playing cards has 13 cards in each of four suits: hearts, clubs, diamonds, and spades. Two cards are chosen f

rom the deck at random. What is the probability of choosing one club and one spade?
Mathematics
1 answer:
Aloiza [94]3 years ago
5 0

Answer:

Probability of choosing one club and one spade = 0.6025

Step-by-step explanation:

Total number of cards= 52 cards

For the first event

Probability of choosing a club

Toatal club = 13 cards

Probability of choosing a club

= 13/52

Probability of choosing a club

= 1/4

Probability of choosing a club

=0.25

For the second event

Probability of choosing a spade

Toatal spade = 13 cards

Probability of choosing a spade

= 13/52

Probability of choosing spadep

= 1/4

Probability of choosing a spade = 0.25

Probability of both = 0.25*0.25

Probability of both = 0.6025

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You are asking for the condition needed for the 
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5 0
3 years ago
Read 2 more answers
Suppose a batch of metal shafts produced in a manufacturing company have a population standard deviation of 1.3 and a mean diame
lbvjy [14]

Answer:

54.86% probability that the mean diameter of the sample shafts would differ from the population mean by more than 0.1 inches

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are 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.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this problem, we have that:

\mu = 208, \sigma = 1.3, n = 60, s = \frac{1.3}{\sqrt{60}} = 0.1678

What is the probability that the mean diameter of the sample shafts would differ from the population mean by more than 0.1 inches

Lesser than 208 - 0.1 = 207.9 or greater than 208 + 0.1 = 208.1. Since the normal distribution is symmetric, these probabilities are equal, so we find one of them and multiply by 2.

Lesser than 207.9.

pvalue of Z when X = 207.9. So

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

By the Central Limit Theorem

Z = \frac{207.9 - 208}{0.1678}

Z = -0.6

Z = -0.6 has a pvalue of 0.2743

2*0.2743 = 0.5486

54.86% probability that the mean diameter of the sample shafts would differ from the population mean by more than 0.1 inches

6 0
3 years ago
-9y - 2 (2 - 7y) + 4
poizon [28]

Answer:

-9y-2(2-7y)+4 expand the brackets using-2

Step-by-step explanation:

-9y-4+14y+4

arrange the like terms

-9y+14y-4+4

=5y becoz -4+4=0

ans=5y

7 0
3 years ago
Read 2 more answers
Which organism is a consumer?<br> Oak tree<br> Rosebush<br> Prairie dog<br> Tomato plant
BlackZzzverrR [31]

Answer:

prairie dog

Step-by-step explanation:

because this eats the other organisims

7 0
2 years ago
Collins Middle School has 240 sixth grade students. If the sixth grade is 30% of the total school, how many students are in the
Masteriza [31]

Answer:

800

Step-by-step explanation:

We can set up a proportion using the information we are given. We know that 240 students corresponds to 30% and that the total number of students, x, corresponds to 100%

\frac{240}{x} = \frac{30}{100}

Cross multiply and solve:

240 * 100 = 30x

24000 = 30x

800 = x

6 0
3 years ago
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