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ANTONII [103]
3 years ago
13

Imagine each letter of the word "Mathematical" is written on individual pieces of paper and placed in a bag. Should you pick a r

andom letter from that bag, what is the probability that you pick a vowel?
Mathematics
2 answers:
Colt1911 [192]3 years ago
8 0

Answer: 5/12

Step-by-step explanation:

The word "Mathematical" has 12 letters, and 5 of them are vowels.

KIM [24]3 years ago
3 0

Probability is the chance or likelihood of a thing to happen. It is the extent to which an event is likely to occur. It is seen that how many times a thing occur out of the total one.

In this example, there are 5 vowels in MATHEMATICAL, these are, A, E A, I, A.

There are total 12 letters in this word. So the probability is 5/12. So there is 5/12 chances of vowels to occur whenever a piece of paper is taken out of the bag.

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Assume that a procedure yields a binomial distribution with a trial repeated n = 5 times. Use some form of technology to find th
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Answer:

P(X = 0) = 0.0263

P(X = 1) = 0.1407

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Step-by-step explanation:

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:

n = 5, p = 0.517

Distribution

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

P(X = 0) = C_{5,0}.(0.517)^{0}.(0.483)^{5} = 0.0263

P(X = 1) = C_{5,1}.(0.517)^{1}.(0.483)^{4} = 0.1407

P(X = 2) = C_{5,2}.(0.517)^{2}.(0.483)^{3} = 0.3012

P(X = 3) = C_{5,3}.(0.517)^{3}.(0.483)^{2} = 0.3224

P(X = 4) = C_{5,4}.(0.517)^{4}.(0.483)^{1} = 0.1725

P(X = 5) = C_{5,5}.(0.517)^{5}.(0.483)^{0} = 0.0369

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