MATH SOLVE

2 months ago

Q:
# A new board game comes with a deck of 20 cards: 5 red, 3 blue, 2 orange, and 10 green.After the deck is shuffled, the player is to choose the top card and note its color, replacethe card, shuffle the deck again, and then choose the top card again and note its color.What is the probability that both cards selected are blue?

Accepted Solution

A:

No offense to the person above me but they are wrong. So first you have to examine the probability of the first card being blue. Since there are 20 total cards, and three are blue, the probability of the first card being blue is 3 out of 20 or 3/20. Now examine the probability of the second card being blue. Since the previous card was replaced, the total number of cards is still 20. Three out of 20 cards are blue (just like before), so the probability of the second card being blue is 3/20. But the answer is NOT 3/20. Because you have to multiply the two probabilities together because it is happening back to back (if that makes sense). So multiply the two fractions. 3/20 times 3/20 = 9/400. So your ANSWER IS 9/400. (I just put it in caps so it’s easy to see) The fraction can’t be simplified any further. Hope this helps!