Answer:
The probability that exactly 2 of the cards are spades is 0.315
Step-by-step explanation:
Given that 6 cards are drawn at random from a standard deck of 52 cards,
we have to find the probability that exactly 2 of the cards are spades.
Total cards=52
Number of cards which are spades=13
Remaining cards=52-13=39
[tex]Probability=\frac{\text{favourable outcomes}}{\text{Total number of outcomes}}[/tex]
[tex]Probability=\frac{_2^{13}\txterm{C}\times _4^{39}\txterm{C}}{_6^{52}\txterm{C}}[/tex]
[tex]Probability=\frac{\frac{13!}{2!11!}\times \frac{39!}{35!4!}}{\frac{52!}{6!46!}}=0.31512988174\sim 0.315[/tex]
Option 3 is correct.
