Hi Mr Simmons,
I am confused by this question about probability (2000 HSC) -could you explain why P(0,1) = 1 and P(1,0) = 0 and how to do the question?
A fair coin is to be tossed repeatedly. For integers r and s, not both zero, let P(r,s) be the probability that a total of r heads are tossed before a total of s tails are tossed so that P(0,1) = 1 and P(1,0) = 0.
(i) Explain why, for r, s≥1,
P(r,s)=½P(r-1,s)+½P(r,s-1).
(ii)Find P(2,3) by using part (i).
(iii)By using induction on n=r+s-1, or otherwise, prove that
P(r,s)=[1/2ⁿ]{(nC0)+(nC1)+…..+(nC(s-1))}
for s≥1
Thanks,
Michael Lin
Hi Mr Simmons,
Hope you are enjoying the school holidays
Are the 99.95ers and first in state invited back to presentation night?
Thanks,
Michael Lin
P.S. you still havent answered my question above
Yes, invites will be sent once we get back to school, i.e. in the next week or so.
The date is Thursday 16th February
As for the question, I must have missed that one, oops!
Thanks!
Hi Mr Simmons,
I am confused by this question about probability (2000 HSC) -could you explain why P(0,1) = 1 and P(1,0) = 0 and how to do the question?
A fair coin is to be tossed repeatedly. For integers r and s, not both zero, let P(r,s) be the probability that a total of r heads are tossed before a total of s tails are tossed so that P(0,1) = 1 and P(1,0) = 0.
(i) Explain why, for r, s≥1,
P(r,s)=½P(r-1,s)+½P(r,s-1).
(ii)Find P(2,3) by using part (i).
(iii)By using induction on n=r+s-1, or otherwise, prove that
P(r,s)=[1/2ⁿ]{(nC0)+(nC1)+…..+(nC(s-1))}
for s≥1
Thanks,
Michael Lin
Hi Mr Simmons,
Hope you are enjoying the school holidays
Are the 99.95ers and first in state invited back to presentation night?
Thanks,
Michael Lin
P.S. you still havent answered my question above
Yes, invites will be sent once we get back to school, i.e. in the next week or so.
The date is Thursday 16th February
As for the question, I must have missed that one, oops!