Question

A die is tossed 1000 times and the outcomes are recorded in the following table. The probability of getting an even number is:

Outcome	1	2	3	4	5	6
Frequency	160	170	140	280	120	130

(a) \[\dfrac{29}{50}\]
(b) \[\dfrac{21}{50}\]
(c) \[\dfrac{11}{25}\]
(d) \[\dfrac{14}{25}\]

Answer 1

Hint: A die is a cube with 6 faces. 3 faces are even 2, 4 and 6. Thus the number of even frequency will be the sum of corresponding values of 2, 4 and 6. Thus probability will be a number of even frequency by the total tossed times.

Complete step-by-step answer:
The even number frequency is equal to the frequency of 2, 4 and 6 from the given table.
\[\therefore \] Even number frequency = 170 + 280 + 130 = 580.
\[\therefore \] The probability of getting an even number = (Even number frequency / Total number of times tossed)
\[\therefore \] Probability of getting an even number = \[\dfrac{580}{1000}=\dfrac{29}{50}\].
Thus we got the required probability as \[\dfrac{29}{50}\].
\[\therefore \] Option (a) is the correct answer.

Note: If we were asked to find an odd number, then we could have calculated the odd number frequency , i.e for (1, 3, 5) by adding the corresponding frequencies from the given table as
= 160 + 140 + 120
= 420
Thus the probability formed will be \[=\dfrac{420}{1000}=\dfrac{21}{25}\].
It is said that a die is tossed 1000 times. We know that a die is a cube of 6 faces. The numbers that are marked on the die are 1, 2, 3, 4, 5, 6.
Thus from the above (2, 4, 6) are even numbers on the face of the die. While (1, 3, 5) are odd numbers on the face of the die.
Thus the total number of times the even number comes up can be represented in set S = {2, 4, 6}.
From the table given,