Question

Three unbiased coins are tossed together, then which of the following is true?

• A. The probability of getting exactly 2 heads is $\frac{1}{2}$
• B. The probability of getting exactly two heads is $\frac{3}{8}$
• C. The probability of getting at least 1 tail is $\frac{3}{8}$
• D. The probability of getting exactly one tail is $\frac{3}{8}$

Answer 1

Answer: (B), (D)

The correct options are
B

The probability of getting exactly two heads is $\frac{3}{8}$

D

The probability of getting exactly one tail is $\frac{3}{8}$

Total possible cases = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT} (where H= Heads, T= Tails)
Number of exactly 2 heads = {HHT, HTH,THH}

= 3

$\therefore$ P (exactly 2 heads) $=\frac{3}{8}$

Number of exactly 1 tail = {HHT, HTH, THH}

= 3
$\therefore$ P(exactly one tail) $=\frac{3}{8}$

Number of cases atleast one tail = {HHT, HTH, HTT, THH, THT, TTH, TTT}

= 7

$\therefore$ P(at least one tail) $=\frac{7}{8}$