Question

A coin is tossed $5$ times. What is the probability that head appears: (i) an even number of times? (ii) an odd number of times( you may regard $0$ as an even number)? (iii) at least $3$ times.

Answer 1

Total possible outcome when a coins is tossed five time will be $32$

HHHHH , HHHHT , HHHTH , HHHTT , HHTHH , HHTTH , HHTHT , HHTTT

HTHHH , HTHHT , HTHTT , HTHTT , HTTHT , HTHTH , HTTTH , HTTTT

THHHH , THHHT , THHTT , THTTH , THTTH , THTHT , THTTT , THHTH

TTHHH , TTHHT , TTHTH , TTHTT , TTTHH , TTTHT , TTTTH , TTTTT

i) Probability that head appears even number of time = $\frac{18}{32}=\frac{9}{16}$

ii)Probability that head appears even number of time = $\frac{14}{32}=\frac{7}{16}$

iii)Probability that head appears at least 3 times = $\frac{14}{32}=\frac{7}{16}$