NCERT Class XI Mathematics - Probability - Solutions
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Question : 28
Total: 54
A fair coin with 1 marked on one face and 6 on the other and a fair die are both tossed. Find the probability that the sum of numbers that turn up is (i) 3 (ii) 12.
Solution:
An experiment consists of tossing a coin marked 1 and 6 on either faces and rolling a die.
∴ The sample space of the experiment is given by
S = {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}
(i) Let E be the event that sum of number is 3.
E = {(1, 2)} ⇒ n(E) = 1
n(S) = 12
∴ P (E) =
(ii) Let F be the event that sum of number is 12.
∴ F = {(6, 6)} ⇒ n(F) = 1 and n(S) = 12
⇒ P (F) =
∴ The sample space of the experiment is given by
S = {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}
(i) Let E be the event that sum of number is 3.
E = {(1, 2)} ⇒ n(E) = 1
n(S) = 12
∴ P (E) =
(ii) Let F be the event that sum of number is 12.
∴ F = {(6, 6)} ⇒ n(F) = 1 and n(S) = 12
⇒ P (F) =
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