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kvasek [131]
2 years ago
10

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 a

nd 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!
Mathematics
1 answer:
tatyana61 [14]2 years ago
6 0

Answer:

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

Step-by-step explanation:

Given

S = \{1,2,3,4,5\}

n(S) = 5

Required

P(x > 1\ and\ x < 2)

P(x > 1\ and\ x < 2) is calculated as:

P(x > 1\ and\ x < 2) = P(x > 1) * P(x < 2)

Since it is a probability with replacement, we have:

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

For x > 1, we have:

x > 1 = \{2,3,4,5\}\\

n(x > 1) = 4

For x < 2, we have:

x < 2 = \{1\}

n(x < 2) = 1

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

becomes

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

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

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