Question

Drawing a card- four cards are drawn from a desk without replacement.Find these probabilities.

A) All cards are jacks
B)All cards are black cards.
C) All cards are hearts

Answer 1

The deck consists of 4 jacks, 26 black cards, and 13 hearts.

There is only 1 way of drawing all 4 jacks:
`\dbinom44=(4!)/(4!(4-4)!)=1`.

There are
`\dbinom{26}4=14,950` ways of drawing 4 black cards.

There are
`\dbinom{13}4=715` ways of drawing 4 hearts.

There are
`\dbinom{52}4=270,725` ways of drawing any 4 cards.

The probabilities are then

a.

`\frac{\binom44}{\binom{52}4}=\frac1{207,725}\approx0.00000369`

b.

`\frac{\binom{26}4}{\binom{52}4}=(46)/(833)\approx0.0552`

c.

`\frac{\binom{13}4}{\binom{52}4}=(11)/(4165)\approx0.00264`