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Andrei [34K]
3 years ago
8

Spinner has six sections of equal shape and size. Each section is either black or white. The table shows the result of an experi

ment when the spinner was spun 76 times:
Result of Spin Black White
Number of Spins 19 57


Based on the data, which of the following best describes the experimental probability of the arrow landing on a black or white section of the spinner?
The spinner is 3 times more likely to land on white.
The spinner is 3 times more likely to land on black.
The information cannot be concluded from the data.
The spinner is equally likely to land on black or white.
Mathematics
2 answers:
lutik1710 [3]3 years ago
6 0

Answer:

The spinner is 3 times more likely to land on white.

Step-by-step explanation:

P( black) = black/ total = 19/76 = .25

P( white) = white/ total = 57/76 = .75

3 out of every 4 spins is white

1 out of every 4 spins is black

3/1 white/black

3 times more likely to get white

Novosadov [1.4K]3 years ago
4 0

Answer:

The spinner is 3 times more likely to land on white.

Step-by-step explanation:

The spinner landed 57 times on white and 19 times on black.

57 is 3 * 19

Answer: The spinner is 3 times more likely to land on white.

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Assume that we have two events, and , that are mutually exclusive. Assume further that we know and . If an amount is zero, enter
sweet [91]

Answer:

Explained below.

Step-by-step explanation:

The complete question is:

Assume that we have two events, A and B, that are mutually exclusive. Assume further that we know P(A) = 0.30 and P(B) =0.40.

What is P(A and B)?

What is P(A | B)?

Is P(A | B) equal to P(A)?

Are events A and B dependent or independent?

A student in statistics argues that the concepts of mutually exclusive events and independent events are really the same, and that if events are mutually exclusive they must be independent. Is this statement accurate?

What general conclusion would you make about mutually exclusive and independent events given the results of this problem?

Solution:

The probability of the two events <em>A</em> and <em>B</em> are:

P(A) = 0.30 and P(B) =0.40

(a)

Compute the value of P (A ∩ B) as follows:

P(A\cap B)=0

This is because mutually exclusive events are those events that cannot occur together.

(b)

Compute the value of P (A | B) as follows:

P(A|B)=\frac{P(A\cap B)}{P(B)}=\frac{0}{0.40}=0

Thus, the value of P (A | B) is 0.

(c)

No, P (A | B) is not equal to the P (A).

(d)

As mentioned in part (a), mutually exclusive events are those events which cannot occur together.

That is, P(A\cap B)=0.

Events A and B are independent  if the chance of their concurrent happening is equivalent to the multiplication of their distinct probabilities.

That is, P(A\cap B)=P(A)\times P(B).

The concepts of mutually exclusive events and independent events are not the same.

(e)

As the it is provided that A and B are mutually exclusive events, we know that P(A\cap B)=0.

Now compute the value of P(A)\times P(B) as follows:

               P(A)\times P(B)=0.30\times 0.40=0.12\neq 0

Thus, the events A and B are not independent.

Thus, if two events are mutually exclusive events they cannot be independent.

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