Note the frequency of two-wheelers, three-wheelers, and four-wheelers passing by your school gate during a specific time interval. Calculate the probability that any one vehicle chosen from the total vehicles observed is a two-wheeler.
(N/A) To find the probability, follow these steps:
$1$. Let $n_1$ be the number of two-wheelers, $n_2$ be the number of three-wheelers, and $n_3$ be the number of four-wheelers observed.
$2$. Calculate the total number of vehicles observed: $N = n_1 + n_2 + n_3$.
$3$. The probability $P$ of selecting a two-wheeler is given by the ratio of the number of two-wheelers to the total number of vehicles.
$4$. Formula: $P(\text{two-wheeler}) = \frac{n_1}{N} = \frac{n_1}{n_1 + n_2 + n_3}$.
$1$. Let $n_1$ be the number of two-wheelers, $n_2$ be the number of three-wheelers, and $n_3$ be the number of four-wheelers observed.
$2$. Calculate the total number of vehicles observed: $N = n_1 + n_2 + n_3$.
$3$. The probability $P$ of selecting a two-wheeler is given by the ratio of the number of two-wheelers to the total number of vehicles.
$4$. Formula: $P(\text{two-wheeler}) = \frac{n_1}{N} = \frac{n_1}{n_1 + n_2 + n_3}$.
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$5$ $3$ $10$ $20$ $25$ $11$ $13$ $7$ $12$ $31$ $19$ $10$ $12$ $17$ $18$ $11$ $32$ $17$ $16$ $2$ $7$ $9$ $7$ $8$ $3$ $5$ $12$ $15$ $18$ $3$ $12$ $14$ $2$ $9$ $6$ $15$ $15$ $7$ $6$ $12$
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$(iii)$ within $\frac{1}{2} \, km$ from her place of work?
| $5$ | $3$ | $10$ | $20$ | $25$ | $11$ | $13$ | $7$ | $12$ | $31$ |
| $19$ | $10$ | $12$ | $17$ | $18$ | $11$ | $32$ | $17$ | $16$ | $2$ |
| $7$ | $9$ | $7$ | $8$ | $3$ | $5$ | $12$ | $15$ | $18$ | $3$ |
| $12$ | $14$ | $2$ | $9$ | $6$ | $15$ | $15$ | $7$ | $6$ | $12$ |
What is the empirical probability that an engineer lives:
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$(iii)$ within $\frac{1}{2} \, km$ from her place of work?
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