HP 10s Instruction Manual page 4
Probability – rearranging items
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- User manual (45 pages) ,
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HP 10s Probability – Rearranging Items
Answer:
2,598,960 different hands.
Example 5: If five cards are dealt from a standard deck of 52 cards, calculate the probability of these five cards
containing four-of-a-kind.
Solution:
The probability is the number of favorable events divided by the number of possible events. There are 13
ranks of four-of-a-kind, the fifth card being any of the remaining 48 cards. The number of possible five-card
hands has been calculated in the previous example: it is given by the combination
probability of being dealt four-of-a-kind is:
The keystroke sequence is:
13*48/52 F 5=
Answer:
0.000240096. Approximately, 1 out of 4165 hands (which is calculated by inverting the result).
Example 6: Find the probability that at least two of 23 people have the same birthday.
Solution:
The probability that at least two of n persons have the same birthday is given by:
example n = 23:
1-365 Ac 23/365L23=
Answer:
0.507297234. The probability is greater than 50%. You can easily verify that for n ≤ 22, the probability is
smaller than 50%, so 23 is the smallest number of persons such that the probability of at least two of them
having the same birthday is greater than 50%!
Example 7: Evaluate the binomial density function f(x) at x=4 for a constant probability of success (p) of 0.49 and 6
Bernoulli trials (n).
n
f
) x (
(
)
Solution:
=
x
6 F 4*.49 L 4*W1-.49XLW4-2X=
Answer:
f(4) = 0.224913711
Example 8: If you flip a coin 10 times, what is the probability that it comes up tails exactly 4 times?
Solution:
It is an application of the previous example. In this case, n = 10, x = 4 and p = 0.5:
10 F 4*.5 L 4*.5LW10-4X=
Answer:
0.205078125. If you flip a coin 10 times, there is a 20.51% chance of seeing heads 4 times.
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possible four - of - a - kind hands
P =
possible five - card hands
!
x
n
x
!
p
(
) p
1
. In our case:
"
"
!
6
4
( f
)
(
)
.
(
4
0
49
1
=
"
"
!
4
- 4 -
52
C
. Therefore, the
5
13 " 48
=
52
(
)
5
365
P
. In this
n
1"
n
365
!
6
4
!
.
)
0
49
HP 10s Probability – Rearranging Items - Version 1.0
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