# Three coins are tossed simultaneously. what is the probability of (i) getting at most two heads (ii) getting at most two tails.

When three coins are tossed simultaneously, the sample space becomes 23 = 8

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

Probability of getting at most two heads:

Let A be the event of getting at most two heads.

So, the favourable outcomes are {HHT,HTH,TTT,THH,TTH,THT,HTT}

Therefore, n(A) = 7

Hence, the probability of getting at most two heads = Number of favourable outcomes/Total number of outcomes = ⅞.

Probability of getting at most two tails:

Let B be the event of getting at most two tails.

So, the favourable outcomes are {HHH, HHT, HTH, THH, TTH, THT, HTT}

Thus, n(B) = 7

Hence, the probability of getting at most two tails = ⅞.