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An experiment has four equally likely outcomes: E1, E2, E3, and E4. (a) What is the probability that E2 occurs? (b) What is the probability that any two of the outcomes occur (e.g., E1 or E3)? (c) What is the probability that any three of the outcomes occur (e.g., E1 or E3 or E4)?

Respuesta :

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Answer with Explanation:

We are given that

E1,E2,E3 and E4 are equally likely outcomes.

Therefore, the probability

[tex]P(E_1)=P(E_2)=P(E_3)=P(E_4)[/tex]

We know that

Sum of all probabilities=1

[tex]P(E_1)+P(E_2)+P(E_3)+P(E_4)=1[/tex]

[tex]P(E_1)+P(E_1+P(E_1)+P(E_1)=1[/tex]

[tex]4P(E_1)=1[/tex]

[tex]P(E_1)=\frac{1}{4}[/tex]

a.[tex]P(E_2)[/tex]=[tex]\frac{1}{4}[/tex]

b.Favorable cases=2

Total outcomes=4

Probability,[tex]P(E)=\frac{favorable\;cases}{Total\;number\;of\;cases}[/tex]

The probability that any two of the outcomes occur=[tex]\frac{2}{4}=\frac{1}{2}[/tex]

c.Favorable cases=3

[tex]P(E)=\frac{3}{4}[/tex]

Answer:

outcomes common to E1 and E2 = [1, 3, 5, 7, 9, 19, 21, 23, 25, 27]

Explanation:

PLATO

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