Question

A simple die is thrown 100 times and the number five appears 14 times. Find the experimental probability of throwing a five, giving your answer as a fraction in its lowest terms.

Answer 1

Answer:

The experimental probability of throwing a five is 0.087.

Step-by-step explanation:

Given:

Number of trials (n) = 100

Number of times 5 appears (x) = 14

Let the event of occurrence of 5 be success and the probability represented by 'p'. So, all the other numbers occurrence is failure and its probability is represented as 'q'.

Probability of success is given as:

$p=\frac{Number\ of\ favorable\ events}{Total\ number\ of\ outcomes}$

Favorable event is occurrence of 5. So, its number is 1 as there is only one 5 in the die. Total outcomes are 6 as there are six numbers. So,

$p=\frac{1}{6}$

Now, probability of failure is given by the formula:

$q=1-p=1-\frac{1}{6}=\frac{5}{6}$

Now in order to find the experimental probability of 14 successes out of 100 trials, we apply Bernoulli's theorem which is given as:

$P(x) = ^nC_xp^xq^{n-x}$

Plug in all the given values and find the probability of 14 successes. This gives,

$P(x=14)=^{100}C_{14}(\frac{1}{6})^{14}(\frac{5}{6})^{100-14}\\\\P(x=14)=0.087$

Therefore, the experimental probability of throwing a five is 0.087.