Question

For each of the following experiments describe the sample space.

A) Three dice are rolled.

B) 5 cards are dealt from a deck.

C) Temperature in front of a building is measured.

D) A student's overall academic performance is assessed.

Answer 1

Part A

Three dice are rolled.

For this experiment, the sample space S is defined as the triplet (a, b, c) where a, b, c takes the values from 1 to 6.

Total number of outcomes = 6*6*6 = 216

This is a discrete sample space.

Part B

5 cards are dealt from a deck.

For this experiment, we can draw first card in 52 way. We do not replace first card. So, we can draw second card in 51 way. Third card is draw in 50 way. Fourth card is drawn in 49 ways. Fifth card is drawn in 48 ways.

So, required number of outcomes in sample space = 52*51*50*49*48 = 311875200

This is a discrete sample space.

Part C

Temperature in front of a building is measured.

For this experiment, the sample space is the range of temperature or the interval of a continuous variable. S = (a, b), where a is minimum possible temperature in front of a building and b is maximum possible temperature.

This is a continuous sample space.

Part D

A student’s overall academic performance is assessed.

For this experiment, the sample space is the range of students GPA or marks. It is nothing but the interval [0, b], where O indicate minimum possible average GPA and b is maximum possible average GPA or marks or academic performance.

This is a continuous sample space.