Solution,
Let, the event of occurring odd number on dice be A and the event of occurring head on a coin be H.
Then, when a dice is rolled,
S = {1, 2, 3, 4, 5, 6} and A = {1, 3, 5}
∴ n(S) = 6 and n(A) = 3
By formula P(A) = \(\frac{n(A)}{n(S)}\)
= \(\frac36\)
= \(\frac12\)
And,
When a coin is tossed,
P(H) = \(\frac12\)
To find: P(A ∩ H)
here, A and H are independent events
∴ P(A ∩ H) = P(A) x P(H)
= \(\frac12\times\frac12\)
= \(\frac14\)
∴ The probability of occurring odd number on dice and head on a coin is 0.25 or \(\frac14\)