Question

Help please?

Answer 1

a) Independent `color(blue)(0.0533 ~~ 5.33%)`
b) Dependent `color(blue)(0.0498 ~~ 4.98%)`

Explanation:

a) In this case, the probabilities are independent because each card has an equal chance of being chosen...`1/52`.

The probability of selecting two face cards with replacement can be calculated like this:
1) There are `3` face cards of each of the `4` colors. `3*4 = 12" face cards"`. This means that in a deck of 52 cards, the probability of picking one face card is `12/52`.
2) With replacement, the second draw will be independent of the first with the same probability so you multiply them together:
`(12/52) * (12/52) ~~ 0.0533 ~~ 5.33%`

b) In this case, the probabilities are dependent because each card does not have an equal chance of being chosen...the first card has a probability of `1/52` but the second card has a probability of `1/51`.
The probability of selecting two face cards without replacement can be calculated like this:
1) There are `3` face cards of each of the `4` colors. `3*4 = 12" face cards"`. This means that in a deck of 52 cards, the probability of picking one face card is `12/52`.
2) Without replacement, the second draw is dependent so the probability will have to be `11/51` because there is one fewer possible face cards and total cards:
`(12/52) * (11/51) ~~ 0.0498 ~~ 4.98%`