Question

Three unbiased coins are tossed simultaneously. Find the probability of getting:

1. exactly two tails
2. at least one head
3. at most two heads

Answer 1

When three unbiased coins are tossed, the possible outcomes are:

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

So, the total number of possible outcomes = 8.

a. Probability of getting exactly two tails:

Favorable outcomes: (HTT, THT, TTH)

Number of favourable outcomes = 3

Probability = `"Number of favourable outcomes"/"Total outcomes"`

Probability of getting exactly two tails = `3/8`

b. Probability of getting at least one head:

Favorable outcomes: (HHH, HHT, HTH, THH, HTT, THT, TTH)
Number of favourable outcomes = 7

Probability of getting at least one head = `7/8`

c. Probability of getting at most two heads:

Favourable outcomes: (HHT, HTH, THH, HTT, THT, TTH, TTT)

Number of favourable outcomes = 7

Probability of getting at least one head = `7/8`