MATH SOLVE

2 months ago

Q:
# If 6 cards are drawn at random from a standard deck of 52 cards, what is the probability that exactly 2 of the cards are spades? 0.038 0.200 0.315 0.465 0.747

Accepted Solution

A:

Answer:The probability that exactly 2 of the cards are spades is 0.315 Β 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=52Number of cards which are spades=13Remaining 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.