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?

6 months ago
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

6 months ago
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

6 months ago
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)

6 months ago
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

6 months ago
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