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A student spins a spinner that has 3 equal sections labeled A, B, and C and then tosses a six-sided number cube.

What is the sample space for this compound event?


A: {A1, B1, C1, A2, B2, C2, A3, B3, C3, A4, B4, C4, A5, B5, C5, A6, B6, C6}

B: {A, B, C, 1, 2, 3, 4, 5, 6}

C: {ABC1, ABC2, ABC3, ABC4, ABC5, ABC6}

D: {A6, B6, C6}

Answer:

{A1, B1, C1, A2, B2, C2, A3, B3, C3, A4, B4, C4, A5, B5, C5, A6, B6, C6}

Step-by-step explanation:

I took the test

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.

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.

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.

Learn more about the Cartesian Product at

https://brainly.com/question/16628099

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