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### BDMO 2017 National round Secondary 1

Posted: Fri Feb 10, 2017 8:36 pm
Bangladesh plays India in a best of five game series. The team that wins $3$ games first wins the series. The series can end after $3$ games, or $4$ games, or $5$ games. If Bangladesh and India are equally strong, calculate

$(a)$ The probability that Bangladesh wins the series in $3$ games.
$(b)$ The probability that Bangladesh wins the series in $4$ games.
$(c)$ The probability that the series ends in exactly $5$ games.

### Re: BDMO 2017 National round Secondary 1

Posted: Fri Feb 02, 2018 2:11 am
(a)$1/8$☺☺☺

### Re: BDMO 2017 National round Secondary 1

Posted: Sat Feb 03, 2018 12:19 am
For $5$ match, result may be of $20$ ways in total. (Excluding unimportant results when series ends in 3/4 matches)

(a)If Bangladesh wins in 3 games, none but the sequence must be:$WWW$. So, the probability=$\frac{1}{20}$

(b)If Bangladesh wins in 4 matches, the sequence may be following: $WWLW, WLWW, LWWW$ (Excluding WWWL), in $3$ ways.
The probability=$\frac{3}{20}$

(c)When the series ends in the last match, the last one must be $W$. So, the sequence: $WWLLW,WLWLW,WLLWW,LWWLW,LWLWW,LLWWW$, in$6$ ways. (Rearranging the first four term with 2 identical W's and 2 identical L)
The probability=$\frac{6}{20}=\frac{3}{10}$

### Re: BDMO 2017 National round Secondary 1

Posted: Sat Feb 03, 2018 11:16 pm
Here are the list of all possibilities of the result of the game(Denoting $W$ and $L$ are the win and lose of Bangladesh):
• $WWW$
• $LLL$
• $LWWW$
• $WLWW$
• $WWLW$
• $WLLL$
• $LWLL$
• $LLWL$
• $WWLLW$
• $WLWLW$
• $WLLWW$
• $LWWLW$
• $LWLWW$
• $LLWWW$
• $WWLLL$
• $WLWLL$
• $WLLWL$
• $LWWLL$
• $LWLWL$
• $LLWWL$
Hence there are $20$ different possible results, not $2^5$

### Re: BDMO 2017 National round Secondary 1

Posted: Sun Feb 04, 2018 2:47 am
Both the solutions are completely wrong. Because the 20 cases aren't equally likely.

### Re: BDMO 2017 National round Secondary 1

Posted: Sun Feb 04, 2018 12:34 pm
My solution may be wrong.But the $20$ cases yield to a result that both team have a probability of $\frac{1}{2}$ to win the series.

### Re: BDMO 2017 National round Secondary 1

Posted: Sun Feb 04, 2018 7:30 pm
Can anyone give the correct solution?

### Re: BDMO 2017 National round Secondary 1

Posted: Tue Feb 06, 2018 1:52 pm
(a) Bangladesh wins the series in $3$ matches iff they win all $3$ of the games. And the probability of that is $\dfrac{1}{8}$.