Question

Suppose a coin is tossed 20 times. The results are shown below. Record the frequency of heads and tails and write each empirical probability as a fraction there are seven heads and 13 tails what’s the empirical probability of both?

Answer 1

Probablility of getting heads: 7/20

Probablility of getting tails: 13/20

Probablility of both: 91/400

Explanation:

The empirical probability of an event is calculated by dividing the frequency of the event by the total number of trials. In this case, we have tossed a coin 20 times and recorded 7 heads and 13 tails.

To calculate the empirical probability of heads, we divide the frequency of heads (7) by the total number of trials (20):

Empirical probability of heads = Frequency of heads / Total number of trials = 7 / 20

To calculate the empirical probability of tails, we divide the frequency of tails (13) by the total number of trials (20):

Empirical probability of tails = Frequency of tails / Total number of trials = 13 / 20

Therefore, the empirical probability of getting both heads and tails is the product of the empirical probabilities of heads and tails:

Empirical probability of both = Empirical probability of heads × Empirical probability of tails

Let's calculate the empirical probabilities:

Probability of heads = 7 / 20

Probability of tails = 13 / 20

Empirical probability of both = (7 / 20) × (13 / 20)

To simplify the fraction, we can cancel out common factors. In this case, there are no common factors to cancel out. Therefore, the empirical probability of both heads and tails is (7 / 20) × (13 / 20), which is equal to 91 / 400.

So, the empirical probability of getting both heads and tails is 91 / 400.