The sample space of the compound event of spinning a spinner and tossing a six-sided number cube is {A1, B1, C1, A2, B2, C2, A3, B3, C3, A4, B4, C4, A5, B5, C5, A6, B6, C6}, the cartesian product of the sample spaces of the two events. Hence, option A is the right choice.
What is a cartesian product?
An ordered set of sets is used to define a Cartesian Product. It's the collection of all conceivable ordered combinations made up of one member from each of the sets.
The set containing all ordered pairs (p, q), where p is an element of P and q is an element of Q, is the Cartesian product of two sets, P and Q, represented as P*Q.
How do we solve the given question?
We are given that a student spins a spinner that has 3 equal sections labeled A, B, and C and then tosses a six-sided number cube.
Let the event of getting something on spinner be X.
∴ Sample space of X = {A, B, C}
Let the event of getting something on the number cube be Y.
∴ Sample space of Y = {1, 2, 3, 4, 5, 6}
The sample space of the compound event is the cartesian product of sample space of X with sample space of Y.
∴ Sample space of compound event = {A, B, C}*{1, 2, 3, 4, 5, 6}
or, Sample space = {A1, B1, C1, A2, B2, C2, A3, B3, C3, A4, B4, C4, A5, B5, C5, A6, B6, C6}.
∴ The sample space of the compound event of spinning a spinner and tossing a six-sided number cube is {A1, B1, C1, A2, B2, C2, A3, B3, C3, A4, B4, C4, A5, B5, C5, A6, B6, C6}, the cartesian product of the sample spaces of the two events. Hence, option A is the right choice.
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