Three coins are tossed simultaneously. Describe the sample space S. Find the probability of getting:

(i) at most 2 heads

(ii) at least 2 heads

(iii) exactly 2 heads

When you toss three coins simultaneously.

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

Total number of outcomes = 8

(i) at most 2 heads

Number of favorable outcomes (Getting at most 2 heads) = 7 (HHT, HTH, THH, HTT, THT, TTH, TTT)

∴ P(getting at most 2 heads) = $\dfrac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \dfrac{7}{8}.$

Hence, the probability of getting at most 2 heads is $\dfrac{7}{8}$.

(ii) at least 2 heads

Number of favorable outcomes (Getting at least 2 heads) = 4 (HHT, HTH, THH, HHH)

∴ P(getting at least 2 heads) = $\dfrac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \dfrac{4}{8} = \dfrac{1}{2}.$

Hence, the probability of getting at least 2 heads is $\dfrac{1}{2}$.

(iii) exactly 2 heads

Number of favorable outcomes (Getting exactly 2 heads) = 3 (HHT, HTH, THH)

∴ P(getting exactly 2 heads) = $\dfrac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \dfrac{3}{8} .$

Hence, the probability of getting exactly 2 heads is $\dfrac{3}{8}$.