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Please help, thanks! Ok so, you pick a card at random, put it back, and then pick another card at random. There are FIVE cards and they are numbered like this: 1, 2, 3, 4, 5. What is the probability of picking a number greater than 1 and then picking a number less than 2? Write the answer as a fraction or whole number. Thank you!

Sagot :

MrRoyal

Answer:

[tex]P(x > 1\ and\ x < 2) = \frac{4}{25}[/tex]

Step-by-step explanation:

Given

[tex]S = \{1,2,3,4,5\}[/tex]

[tex]n(S) = 5[/tex]

Required

[tex]P(x > 1\ and\ x < 2)[/tex]

[tex]P(x > 1\ and\ x < 2)[/tex] is calculated as:

[tex]P(x > 1\ and\ x < 2) = P(x > 1) * P(x < 2)[/tex]

Since it is a probability with replacement, we have:

[tex]P(x > 1\ and\ x < 2) = \frac{n(x > 1)}{n(S)} * \frac{n(x < 2)}{n(S)}[/tex]

For x > 1, we have:

[tex]x > 1 = \{2,3,4,5\}\\[/tex]

[tex]n(x > 1) = 4[/tex]

For x < 2, we have:

[tex]x < 2 = \{1\}[/tex]

[tex]n(x < 2) = 1[/tex]

[tex]P(x > 1\ and\ x < 2) = \frac{n(x > 1)}{n(S)} * \frac{n(x < 2)}{n(S)}[/tex]

becomes

[tex]P(x > 1\ and\ x < 2) = \frac{4}{5} * \frac{1}{5}[/tex]

[tex]P(x > 1\ and\ x < 2) = \frac{4}{25}[/tex]

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