Question

Two fair dice, one blue and one red, are tossed, and the up face on each die is recorded. Define the following events: E:{ The numbers are equal } F:{ The sum of the numbers is even } Find the following probabilities: (a) P(E)= 1/6 (b) P(F)= 1/2 (c) P(E∩F)=

Answer 1

Answer:

(i) 1/6

(ii) 1/2

(iii) 1/6

Explanation:

When two fair dice are tossed,

Total possible outcomes,

n(S) = 6 × 6 = 36,     ( ∵ outcome when a dice is tossed = 6 )

(i) If E = {The numbers are equal }

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

⇒ n(E) = 6,

$\text{Probability}=\frac{\text{Favourable outcomes}}{\text{Total outcomes}}$

Thus,

$P(E) =\frac{n(E)}{n(S)}=\frac{6}{36}=\frac{1}{6}$

(ii) Since, even + even = even and odd + odd = even,

If F = {The sum of the numbers is even}

F = {(1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6), (1, 3), (1, 5), (2, 4), (2, 6), (3, 1), (3, 5), (4, 2), (4, 6), (5, 1), (5, 3), (6, 2), (6, 4)}

⇒ n(F) = 18,

$P(E) =\frac{18}{36}=\frac{1}{2}$

(iii) E∩F = E,

⇒ n(E∩F) = 6,

$P(E\cap F) =\frac{1}{6}$