ENGRD2700
Basic Engineering Probability and Statistics
Fall 2011
Recitation 3: 912 September 2011
Solutions
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.
1. In 5–card poker, a straight consists of five cards with adjacent denominations (e.g. 9
♣
–10
♥
–J
♥
– Q
♠
–
K
♣
). Aces can be high or low, i.e. we could have 10–J–Q–K–A or A–2–3–4–5 but not Q–K–A–2–3.
(a) What is the probability that a 5–card hand will be a straight with high card 10?
4
5
/
(
52
5
)
(need 10–9–8–7–6, have 4 choices for each card)
(b) What is the probability that a hand will be a straight?
10
·
4
5
/
(
52
5
)
(the previous probability is the probability of getting a straight with high card
n
;
n
can range from 5 to A)
(c) What is the probability that a hand will be a straight flush (a straight with all the cards in the
same suit)?
P
(straight flush with high card
n
) = 4
/
(
52
5
)
, so
P
(straight flush) = 10
·
4
/
(
52
5
)
.
2. A person can have any number of phobias. We consider three phobias in particular. Let
A
1
denote
the event that a person has Phobia 1 (Apocolocynposis—fear of being turned into a pumpkin). Let
A
2
denote the event that a person has Phobia 2 (Anatidaephobia—fear of being watched by ducks). Let
A
3
denote the event that a person has Phobia 3 (Hippolarconinsomiaphobia—fear of one’s pyjamas
being stolen by hippos). Suppose we have determined the following probabilities:
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