In each of the following, find the cardinality of the sample space S and of the

Question

In each of the following, find the cardinality of the sample space S and of the specified event E. (a) 3 coins are tossed: E The result is no heads. n (S) = n (E) = (b) A die is thrown: E The result is an odd number. n (S) = n (E) = (c) A pair of distinguishable dice are thrown and the sum of the numbers facing up is noted: E The result is less than 8. n(S) = n (E) = (d) A pair of indistinguishable dice are thrown and the sum of the numbers facing up is noted: E The result is equal to 8. n (S) = n (E) =

Explanation / Answer

a)
‘S’ be the sample space.
Then S = { HHH, HHT, HTH, THH, HTT, THT, TTH, TTT }
n(S ) = 8

n(E) = 1

b)

Possible outcomes in a throw of a dice are 1,2,3,4,5&6.

Therefore, n(S) = 6
n(E) = 3

c)

There are 36 equally likely outcomes:

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

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

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

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

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

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

n(s) = 36

n(E) = 21

d)

There are 36 equally likely outcomes:

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

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

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

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

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

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

n(s) = 36

n(E) = 5

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