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Natasha2012 [34]
3 years ago
13

What is the probability that a random permutation of the letters in MATHEMATICS contains the word TEA (with those three letters

appearing consecutively)?
Mathematics
1 answer:
Wewaii [24]3 years ago
5 0

Answer:

The probability that a random permutation of the letters in MATHEMATICS contains the word TEA is 0.04.

Step-by-step explanation:

First compute the number of permutations of the word MATHEMATICS.

There are a total of 11 letters.

And there are 2 Ms, 2 As and 2 Ts

Number of permutations of MATHEMATICS = \frac{11!}{2!\times2!\times2!} = 4989600

Now, if the letters TEA occur together in the same order then the word may be of the form: (TEA)MHMATICS.

There are a total of 9 letters.

The letters TEA is treated as only one letter.

In this case there are 2 Ms.

Number of permutations of (TEA)MHMATICS = \frac{9!}{2!} = 181440

The probability that the letters TEA occur together is:

\frac{Number\ of\ permutations\ of\ MATHEMATICS}{Number\ of\ permutations\ of\ (TEA)MHMATICS} = \frac{181440}{4989600} \\=0.0363636\\\approx0.04

Thus, the probability that a random permutation of the letters in MATHEMATICS contains the word TEA is 0.04.

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The 5 - number summary of the distribution obtained from the boxplot is :

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  • Maximum = 85
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Firstly, we need to extract the values for the amount spent by females :

20, 25, 25, 35, 37, 38, 39, 43, 45, 46, 50, 53, 60, 70, 85, 100

The five number summary include ;

  • Minimum, lower Quartile, Median, Upper Quartile and Maximum values.

Rearranging the data in ascending order :

20, 25, 25, 35, 37, 38, 39, 43, 45, 46, 50, 53, 60, 70, 85, 100

The boxplot clearly and easily gives the five number summary of the distribution :

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  • Lower quartile = 35 (starting point of the box)
  • Median = 44 (vertical line in between the box)
  • Upper quartile = 58 (endpoint of the box)
  • Maximum = 85 (endpoint of the upper whisker).

Outlier :

  • Lower boundary = LOWER QUARTILE - (1.5 × IQR)
  • Upper boundary = UPPER QUARTILE + (1.5 × IQR)
  • IQR = UPPER QUARTILE - LOWER QUARTILE
  • IQR = (58 - 35) = 23

Lower boundary = 35 - (1.5 × 23) = 0.5

Upper boundary = 58 + (1.5 × 23) = 92.5

  • The point denoted by a dot on the boxplot is an outlier = 100

Hence, values lesser than 0.5 or greater than 92.5 are outliers.

Therefore, 100 is an outlier.

Learn more : brainly.com/question/24582786

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