In tossing a die 10 times, the outcomes are noted.

1, 3, 2, 1, 5, 6, 3, 4, 1, 5

S1: The empirical probability of getting a 1 is $\frac{1}{6}$ .

S2: The theoretical probability of getting a 1 is $\frac{1}{6}$ .

S1 and S2 are false

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S1 and S2 are true

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S1 is false and S2 is true

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S1 is true and S2 is false

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Solution

The correct option is C
S1 is false and S2 is true

Empirical probability = $\frac{n u m b e r o f t r i a l s i n w h i c h t h e e v e n t h a p p e n e d}{t o t a l n u m b e r o f t r i a l s}$ = $\frac{3}{10}$ = 0.3

Theoretical probability = $\frac{n u m b e r o f o u t c o m e s f a v o u r a b l e t o e v e n t}{t o t a l n u m b e r o f p o s s i b l e o u t c o m e s}$ = $\frac{1}{6}$ = 0.167

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6

A die thrown 300 times and the outcomes are noted as given below:

$\begin{matrix} Outcome & 1 & 2 & 3 & 4 & 5 & 6 Frequency & 60 & 72 & 54 & 42 & 39 & 33 \end{matrix}$

When a die is thrown at random, what is the probability of getting a

(i) 3?

(ii) 6?

(iii) 5?

(iv) 1?

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