sample space

Question

During an experiment, 3 coins were tossed once

Part A: Give the sample space to show all possible outcomes for tossing 3 coins one time, using the letter H when a coin faces "heads" up, and the letter T when it faces "tails"

Part B: Based on your answer to part A, how many outcomes consist of 3 heads or 3 tails?

Part C: During a math class, each of 24 students tossed three coins once. Based on your answer to Part B, how many students would you expect to get a result of 3 heads or 3 tails?

Answer 1

A) There are 3 coins and each one is tossed once. We know that a coin only has 2 possible outcomes, H or T. The total possible amount of outcomes is equal to 2ⁿ, where n is equal to the number of flips and 2 is equal to the possible outcomes, H or T. In this question n is equal to 3 because we flip 3 coins once and want to know the total number of outcomes in that sequence. So the answer is 2³=8 possible outcomes,

 

HHH, HHT, HTH, THH, TTT, TTH, THT, HTT

 

B) By looking at the total possible outcomes from the previous answer we can tell that only 2 of the 8 outcomes have 3 Heads or 3 Tails.

 

C) (2/8)*24 =>

    (1/4)*24 =>

     24/4     =>   6 students.

 

We are specifically looking for 2 of the 8 outcomes, HHH or TTT. This means we are looking for (2/8), which simplifies to (1/4), of the possible outcomes. If 24 students try the experiment we can expect that (1/4) of the 24 students should flip a HHH or TTT, which equals 6 students.

Answer 2

part A) HHH, HHT, HTH, HTT,TTT, TTH,THT,THH. ( 2³)

 

part B) 2

 

part C)  chances of throwing all heads or all tails is 2/8 = 1/4

            multiply 1/4 by 24 students 6