Ask your own question, for FREE!
Mathematics 21 Online
kinzakenny:

13. Four cards are drawn from a standard deck. No cards are returned. a) Which is more likely: Event A: drawing a straight (four consecutive cards e.g. 5, 6, 7, 8), or Event B: drawing four consecutive Queens? b) How does your answer change if cards are returned after each draw?

Vocaloid:

hm. I wouldn't know exactly how to do the calculations but drawing ~any~ four consecutive cards is much more likely because there's so many more combinations of straights (2,3,4,5, or 3,4,5,6, etc.) whereas there are only 4 queens

Vocaloid:

as for how the answer changes, event A will still be more likely than B but the probabilities of events A and B both decrease since you are leaving more cards in the deck, and thus, decreasing the probability of drawing any individual desired card

Vocaloid:

I can attempt the calculations (not sure if I'm doing this right but I'll try) if we count aces as low then A 2 3 4 2 3 4 5 3 4 5 6 4 5 6 7 5 6 7 8 6 7 8 9 7 8 9 10 8 9 10 J 9 10 J Q 10 J Q K so 10 possibilities for straights for the first calculation we are assuming non-replacement so the probability of drawing A 2 3 4 is (4/52)(4/48)(4/44)(4/40) there are 10 possible ways this can happen so probability of drawing straight = 10(4/52)(4/48)(4/44)(4/40) the queens are a lot easier, since we only have 4 queens (4/52)(3/51)(2/50)(1/49) showing mathematically that P(event A) > P(event B)

Vocaloid:

if you'd like you can try doing the calculations for b, it's the same logic but the denominators will all be 52 since we are replacing cards this time

Can't find your answer? Make a FREE account and ask your own questions, OR help others and earn volunteer hours!

Join our real-time social learning platform and learn together with your friends!
Can't find your answer? Make a FREE account and ask your own questions, OR help others and earn volunteer hours!

Join our real-time social learning platform and learn together with your friends!