Question

The probability of getting a head when a biased coin is tossed is . The coin is tossed three times. Find the following probabilities and select the correct solution. P(three tails) = . P(two tails followed by one head) = .

Answer 1

a) P(three tails) =
`(1)/(8)`

b) P(two tails followed by one head) =
`(1)/(8)`

Explanation:

coin is tossed three times so, outcome is

HHH, TTT, HTH, THH, HHT, THT, TTH, HTT.

Hence sample space will be

S = {HHH, TTT, HTH, THH, HHT, THT, TTH, HTT}

chance of getting three tails is '1' i.e. TTT

hence,

P(three tails) =
`(1)/(8)`

two tails followed by one head is TTH

so, chance of getting that outcome is also '1'

hence,

P(two tails followed by one head) =
`(1)/(8)`