Question

A dice is rolled. If an odd number appears on the die then a coin is tossed up, otherwise a die is rolled. If the coin shows head then again toss a coin otherwise roll a die. The probability of getting two heads is equal to

• A.
  
  $\frac{1}{13}$
• B.
  $\frac{3}{7}$
• C.
  $\frac{1}{14}$
• D.
  $\frac{5}{7}$

Answer 1

The correct option is C

$\frac{1}{14}$
The possible outcomes are:

(1, H, H), (1, H, T), (1, T, 1), (1, T, 2),
(1, T, 3), (1, T, 4), (1, T, 5), (1, T, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5),
(2, 6), (3, H, H), (3, H, T), (3, T, 1),
(3, T, 2), (3, T, 3), (3, T, 4), (3, T, 5),
(3, T, 6), (4, 1), (4, 2), (4, 3), (4, 4),
(4, 5), (4, 6), (5, H, H), (5, H, T), (5, T, 1), (5, T, 2), (5, T, 3), (5, T, 4), (5, T, 5),
(5, T, 6), (6, 1), (6, 2), (6, 3), (6, 4),
(6, 5), (6, 6)

$\therefore$ Total number of outcomes = 42

Also, the outcomes having two heads are (1, H, H), (3, H, H), (5, H, H).

$\therefore$ Number of outcomes having two heads = 3

$\therefore \text{P(getting 2 heads)}=\frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}=\frac{3}{42}=\frac{1}{14}$

Hence, the correct answer is option c.