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题目7d3svk 历史解析

V20130922版本

The price is up by exactly $3 in 5 days means that 4 days it went up (+4$) and one day it went down (-1$).

UUUUD --> .

Answer: C.

If the probability of a certain event is , then the probability of it occurring times in -time sequence is:

In our case probability of having 4 days when price went up (4U) and one day

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V20140408版本

The price is up by exactly $3 in 5 days means that 4 days it went up (+4$) and one day it went down (-1$).

UUUUD --> $P(U=4)=C^4_5*(\frac{1}{2})^4*\frac{1}{2}=\frac{5}{32}$ .

Answer: C.

If the probability of a certain event is $p$ , then the probability of it occurring $k$ times in $n$ -time sequence is: $P = C^k_n*p^k*(1-p)^{n-k}$

In our case probability of having 4 days when price went up (4U) and one day when price went down (D):
$n=5$ (5 days);
$k=4$ (4 days when price wen t up);
$p=\frac{1}{2}$ (probability of price going up is 1/2).

So, $P = C^k_n*p^k*(1-p)^{n-k}=C^4_5*(\frac{1}{2})^4*(1-\frac{1}{2})^{(5-4)}=C^4_5*(\frac{1}{2})^5$

OR: probability of scenario U-U-U-U-D is $(\frac{1}{2})^4*(\frac{1}{2})^4=(\frac{1}{2})^5$ , but U-U-U-U-D can occur in different ways:

U-U-U-U-D;
U-U-U-D-U
U-U-D-U-U
U-D-U-D-U
D-U-U-U-U;

5 ways (# of permutations of five letters U-U-U-U-D, which is $\frac{5!}{4!}=5=C^4_5$ ).

Hence $P=\frac{5!}{4!}*(\frac{1}{2})^5$ .

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