1. An experiment consists of tossing 2 coins and a die. List the elements of the following and determine n(S) for the sample space and (E) for the given event.
a. Sample space
b. The event that a head appears on both coins and a number less than 5 appears on the die.
2. Walter rolled a die 120 times and the results showed that the number 6 appeared 42 times. What is the experimental probability that.
a. The die will show 6?
b. The die will not show the number 6?
a. Sample space
b. The event that a head appears on both coins and a number less than 5 appears on the die.
2. Walter rolled a die 120 times and the results showed that the number 6 appeared 42 times. What is the experimental probability that.
a. The die will show 6?
b. The die will not show the number 6?
Answers & Comments
Answer:
1)
a. The sample space consists of all possible outcomes of tossing 2 coins and a die. Let's list the elements:
For the two coins, we have the following possibilities:
Coin 1: Head (H), Tail (T)
Coin 2: Head (H), Tail (T)
For the die, we have the numbers 1 to 6.
Combining the outcomes of the two coins and the die, we get the following elements of the sample space:
Sample space (S):
{(H, H, 1), (H, H, 2), (H, H, 3), (H, H, 4), (H, H, 5), (H, H, 6),
(H, T, 1), (H, T, 2), (H, T, 3), (H, T, 4), (H, T, 5), (H, T, 6),
(T, H, 1), (T, H, 2), (T, H, 3), (T, H, 4), (T, H, 5), (T, H, 6),
(T, T, 1), (T, T, 2), (T, T, 3), (T, T, 4), (T, T, 5), (T, T, 6)}
The sample space, S, contains a total of 24 possible outcomes.
b. The event is defined as a head appearing on both coins and a number less than 5 appearing on the die. Let's list the elements that satisfy this condition:
Event (E):
{(H, H, 1), (H, H, 2), (H, H, 3),
(H, T, 1), (H, T, 2), (H, T, 3)}
The event, E, contains a total of 6 outcomes.
Therefore:
n(S) = 24 (the total number of outcomes in the sample space)
n(E) = 6 (the total number of outcomes in the event)
2)
To calculate the experimental probability:
a. The experimental probability of the die showing a 6 is found by dividing the number of times a 6 appeared by the total number of rolls:
Experimental probability of rolling a 6 = Number of times 6 appeared / Total number of rolls
Experimental probability of rolling a 6 = 42 / 120
Experimental probability of rolling a 6 = 0.35 (or 35%)
b. The experimental probability of the die not showing the number 6 can be calculated by subtracting the probability of rolling a 6 from 1 (since it represents the complement event):
Experimental probability of not rolling a 6 = 1 - Experimental probability of rolling a 6
Experimental probability of not rolling a 6 = 1 - 0.35
Experimental probability of not rolling a 6 = 0.65 (or 65%)
Therefore:
a. The experimental probability of the die showing a 6 is 0.35 or 35%.
b. The experimental probability of the die not showing the number 6 is 0.65 or 65%.
Step-by-step explanation: