Question

a die is rolled and coin is tossed simultaneously find the the probability that the die shows and odd number and the coin shows a head

Answer 1

Sample space:

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

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

• Sample space is defined as set of total possible outcomes.
• Number refers the number on die.
• T refers Tail and H refers Head.

Total no. of possible outcomes = 12

Favourable outcome(Event) = Die shows an odd number and the coin shows a head. { (1,H) , (3,H) , (5,H) }

No. of favourable outcomes = 3

• Probability of event = No. of favourable outcomes/Total no. of possible outcomes

P(E) = 3/12 = 1/4

Answer 2

(S) = {1H, 2H, 3H, 4H, 5H, 6H, 1T, 2T, 3T, 4T, 5T, 6T}

n(S) = {12}

Event A:- the die shows and odd number and the coin shows a head.

(A) = { 1H, 3H, 5H}

n(A) = {3}

p(A) =

$\frac{n(a)}{n(s)} = \frac{3}{12} = \frac{1}{4} - - - - - (1)$

probability is :-

$\frac{1}{4}$