Question

2. What is the experimental probability of rolling a 4

3. Getting at least one tail
Experimental and theoretical

Answer 1

1. 40%

2. The theoretical probability is 3% greater than the experimental probability.

Explanation:

1. Lets define experimental probability first.

Experimental probability is the probability of an event's occurrence when the experiment was conducted.

The number cube is rolled 20 times, so our sample space is 20.

And the number 4 came in result 8 times, so the the event space is 8.

So,

Experimental Probability = 8/20

=> 0.4

Converting into percentage will give:

=> 40%

So the first option is correct.

2. First we have to find the theoretical probability of getting at least one tail when two coins are tossed

The sample space is {HH, HT, TH, TT}

3 out of these 4 outcomes contain at least one tail

So the theoretical probability of getting at least one tail is: 3/4

=> 0.75 or 75%

Now for the experimental probability,

The total sample space is 28+22+34+16 = 100

The number of favorable outcomes are(Which contain at least one tail):

22+34+16 = 72

So, experimental probability of getting at least one tail = 72/100

=> 0.72 or 72%

We can see that the theoretical probability is 3% greater than the experimental probability. So second option is correct..

Answer 2

1. 40%

2. The theoretical probability is 3% greater than the experimental probability.

Explanation:

We are informed that a number cube is rolled 20 times and the number 4 is rolled 8 times. The experimental probability of rolling a 4 is;

(the number of times a 4 was rolled)/(total number of rolls)

8/20 = 0.4

0.4*100 = 40%

The experimental probability of obtaining at least one tails, one or more tails, is represented in mathematical notation as;

P(HT or TH or TT)

The above events are mutually exclusive, thus;

P(HT or TH or TT) = P(HT) + P(TH) + P( TT)

= (22+34+16)/(28+22+34+16)

= 0.72 = 72%

On the other hand, the theoretical probability of obtaining at least one tails,

P(HT or TH or TT) = 3/4

= 75%

This is because there is at least one tail in 3 out of 4 possible outcomes.

Therefore, it is true to say that the theoretical probability is 3% greater than the experimental probability.