Question

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?

Answer 1

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

Answer 2

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

Answer 3

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)

Answer 4

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