Question

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!

Answer 1

`P(x > 1\ and\ x < 2) = (4)/(25)`

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) = (n(x > 1))/(n(S)) * (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) = (n(x > 1))/(n(S)) * (n(x < 2))/(n(S))`

becomes

`P(x > 1\ and\ x < 2) = (4)/(5) * (1)/(5)`

`P(x > 1\ and\ x < 2) = (4)/(25)`