Question

A die is thrown 100 times and outcomes are noted as given below:

Outcome:	1	2	3	4	5	6
Frequency:	21	9	14	23	18	15

If a die is thrown at random, find the probability of getting a/an.
(i) 3
(ii) 5
(iii) 4
(iv) Even number
(v) Odd number
(vi) Number less than 3.

Answer 1

Total number of trials = 100

Number of times "1" comes up = 21
Number of times "2" comes up = 9
Number of times "3" comes up = 14
Number of times "4" comes up = 23
Number of times "5" comes up = 18
Number of times "6" comes up = 15


(i) Probability of getting 3

=$\frac{\mathrm{frequency}\mathrm{of}3}{\mathrm{Total}\mathrm{no}.\mathrm{of}\mathrm{trails}}=\frac{14}{100}=0.14$

(ii) Probability of getting 5

= $\frac{\mathrm{frequency}\mathrm{of}5}{\mathrm{Total}\mathrm{no}.\mathrm{of}\mathrm{trails}}=\frac{18}{100}=0.18$

(iii) Probability of getting 4

=$\frac{\mathrm{frequency}\mathrm{of}4}{\mathrm{Total}\mathrm{no}.\mathrm{of}\mathrm{trails}}=\frac{23}{100}=0.23$

(iv) Frequency of getting an even no. = Frequency of 2 + Frequency of 4 + Frequency of 6 = 9+ 23 + 15 = 47

Probability of getting an even no. =$\frac{\mathrm{frequency}\mathrm{of}\mathrm{even}\mathrm{no}.}{\mathrm{Total}\mathrm{no}.\mathrm{of}\mathrm{trails}}=\frac{47}{100}=0.47$


(v) Frequency of getting an odd no. = Frequency of 1 + Frequency of 3 + Frequency of 5 = 21+ 14 + 18 = 53

Probability of getting an odd no. =$\frac{\mathrm{frequency}\mathrm{of}\mathrm{odd}\mathrm{no}.}{\mathrm{Total}\mathrm{no}.\mathrm{of}\mathrm{trails}}=\frac{53}{100}=0.53$


(vi) Frequency of getting a no. less than 3 = Frequency of 1 + Frequency of 2= 21 + 9 = 30

Probability of getting a no. less than 3

=$\frac{\mathrm{frequency}\mathrm{of}\mathrm{no}.\mathrm{less}\mathrm{than}3}{\mathrm{Total}\mathrm{no}.\mathrm{of}\mathrm{trails}}=\frac{30}{100}=0.30$