Question

A lopsided coin has a probability of 1/3 for coming up heads and 2/3 for coming up tails. On average, how many flips of this coin are needed to have both heads and tails appear at least once? Give your answer as a reduced fraction.

Answer 1

Answer with explanation:

For a Lopsided coin ,probability of getting Head is equal to
`(1)/(3)` For a Lopsided coin ,probability of getting Tail is equal to
`(1)/(3)`.

→Probability of getting Tail > Probability of getting Head

→Coin is heavier from tail side and lighter from Head side.

→→We have to Calculate number of flips of coin that is needed to have both heads and tails appear at least once.

`\rightarrow P(\text{Head})=(1)/(3)\\\\ (1)/(3) * x=1\\\\x=3\\\\\rightarrow P(\text{Tail})=(2)/(3)\\\\ (2)/(3) * y=1\\\\y=(3)/(2)`

→We need to find common multiple of 3 and
`(3)/(2)`.

Least common multiple of 3 and
`(3)/(2)` is 6.

→So,on Average number of flips of this coin are needed to have both heads and tails appear at least once=6 tosses