Question

A person draws 3 cards without replacement from a standard? 52-card deck. Find the probability of drawing exactly two 4, 5, 6, or 7 s

Answer 1

The probability of drawing exactly two 4, 5, 6, or 7 s is
`(216)/(1105)`.

Explanation:

In a standard deck the total number of cards is 52.

There are 4 different suits and each suit have 13 different cards.

13 different cards for one spaed , 13 different card of club, 13 different card of diamond and 13 different card of heart.

So we have 4 card of each number.

The total card of 4,5,6 and 7 s are

`4* 4=16`

The number of cards which are not 4,5,6 and 7 s,

`52-16=32`

Use combination to find the probability of drawing exactly two 4, 5, 6, or 7 s.

We have to select 2 card from 16 card, 1 card from another 32 card and 3 card from 52 card.

`P=\frac{\text{possible outcomes}}{\text{Total number of outcomes}}`

`P=(^(16)C_(2)* ^(36)C_(1))/(^(52)C_(3))`

`^(n)C_(r)=(n!)/(r!(n-r)!)`

`P=(120* 36)/(22100)`

`P=(216)/(1105)`

Therefore, the probability of drawing exactly two 4, 5, 6, or 7 s is
`(216)/(1105)`.