Question

(1) Describe the difference between empirical and theoretical probability.
(2) Find the theoritical probability of tossing three coins and getting 2 heads, 1 tail.
(3) Toss three coins at once 50 times and record the out come of getting 2 heads, 1 tail.
(4)) Based on your observations, give the empirical probability of each result.

Answer 1

(1)

Empirical probability is the experimental probability of an event, given by the ratio of the number of outcomes in which the specified event occurs to the total number of events, whereas the theoretical probability is the likelihood of the event occurring given by the ratio of the number of favorable outcomes to th total number of possible outcomes.

(2)

Total number of events:

HHH, HHT, HTH, THH, HTT, THT, TTH, TTT : 8 Nos.

Number of favorable events: 2 H & 1 T:

HHT, HTH, THH: 3 Nos.

So,

the theoretical probability of tossing three coins and getting 2 heads, 1 tail = 3/8 = 0.375

So,

Answer is:

0.375

(3)

Suppose we toss three coins at once 50 times and record the out come of getting 2 heads, 1 tail as follows:

Out of total of 50 trials, the observed number of out come of getting 2 heads, 1 tail = 20

(4)

Based on our observations, the empirical probability of the result. is got as follows:

20/50 = 0.4

So,

Answer is:

0.4