Question

What’s the probability of the following series of events; rolling a 7 on a fair set of 2 dice, followed by flipping a “heads” on a fair coin, followed by selecting the ace of spades from a fairly shuffled deck of 52 cards?

	a.	0.0371
	b.	0.0016
	c.	0.0351
	d.	0.0518
	e.	0.3333

Answer 1

1st event
sample space of two dice rolled simultaneously

(1,1)	(1,2)	(1,3)	(1,4)	(1,5)	(1,6)
(2,1)	(2,2)	(2,3)	(2,4)	(2,5)	(2,6)
(3,1)	(3,2)	(3,3)	(3,4)	(3,5)	(3,6)
(4,1)	(4,2)	(4,3)	(4,4)	(4,5)	(4,6)
(5,1)	(5,2)	(5,3)	(5,4)	(5,5)	(5,6)
(6,1)	(6,2)	(6,3)	(6,4)	(6,5)	(6,6)

Total sample space = 36
Sum of 7 can be seen by 6 rolls
Favourable outcomes (sum of 7) = 6
p(sum of 7) = 6/36 = 1/6

2nd event

while flipping a coin, we have two sample space=heads & tails (2)
P(head) = 1/2

3rd event

shuffled deck of 52 cards
P(Ace of Spade) = 1/52

overall probability = (1/6)*(1/2)*(1/52) = 0.0016 Option B

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