Answer:
The probability of drawing exactly two 4, 5, 6, or 7 s is [tex]\frac{216}{1105}[/tex].
Step-by-step 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
[tex]4\times 4=16[/tex]
The number of cards which are not 4,5,6 and 7 s,
[tex]52-16=32[/tex]
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.
[tex]P=\frac{\text{possible outcomes}}{\text{Total number of outcomes}}[/tex]
[tex]P=\frac{^{16}C_{2}\times ^{36}C_{1}}{^{52}C_{3}}[/tex]
[tex]^{n}C_{r}=\frac{n!}{r!(n-r)!}[/tex]
[tex]P=\frac{120\times 36}{22100}[/tex]
[tex]P=\frac{216}{1105}[/tex]
Therefore, the probability of drawing exactly two 4, 5, 6, or 7 s is [tex]\frac{216}{1105}[/tex].
