Question

agnes has a weighted coin so that heads come up 2/3 of the time.she tosses her coin five times. what is the probability that heads will appear for the first time on toss 5

Answer 1

If heads appears for the first time on toss 5, then the first four tosses must all be tails.

The probability of tails is 1-(2/3) = 1/3.

Answer 2

So the first four tosses must all be tails, then toss 5 is heads:
\[P = \frac{ 1 }{ 3 } \times \frac{ 1 }{ 3 } \times \frac{ 1 }{ 3 } \times \frac{ 1 }{ 3 } \times \frac{ 2 }{ 3 } \]

Answer 3

that what i did

Answer 4

q^1-i * p

which p=2/3
q=1-2/3
i=5

then

(1/3)^4 * 2/3