To know the opinion of the students about the subject statistics,a survey of $200$ students was conducted. The data is recorded in the following table.
Opinion Number of students Like $135$ Dislike $65$
Find the probability that a student chosen at random:
$(i)$ likes statistics,$(ii)$ does not like it.
| Opinion | Number of students |
| Like | $135$ |
| Dislike | $65$ |
Find the probability that a student chosen at random:
$(i)$ likes statistics,$(ii)$ does not like it.
- A$\frac{27}{40}, \frac{13}{40}$
- B$\frac{29}{50}, \frac{13}{50}$
- C$\frac{27}{80}, \frac{13}{80}$
- D$\frac{27}{95}, \frac{13}{36}$
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The record of a weather station shows that out of the past $250$ consecutive days,its weather forecasts were correct $175$ times.
$(i)$ What is the probability that on a given day it was correct?
$(ii)$ What is the probability that it was not correct on a given day?
$(i)$ What is the probability that on a given day it was correct?
$(ii)$ What is the probability that it was not correct on a given day?
Medium
View SolutionAsk all the students in your class to write a $3-$digit number. Choose any student from the room at random. What is the probability that the number written by her/him is divisible by $3$? Remember that a number is divisible by $3$,if the sum of its digits is divisible by $3$.
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View SolutionThree coins are tossed simultaneously $200$ times with the following frequencies of different outcomes:
Outcome $3$ heads $2$ heads $1$ head No head Frequency $23$ $72$ $77$ $28$
If the three coins are simultaneously tossed again,compute the probability of $2$ heads coming up.
| Outcome | $3$ heads | $2$ heads | $1$ head | No head |
| Frequency | $23$ | $72$ | $77$ | $28$ |
If the three coins are simultaneously tossed again,compute the probability of $2$ heads coming up.
Medium
View SolutionThe distance (in $km$) of $40$ engineers from their residence to their place of work were found as follows.
$5$ $3$ $10$ $20$ $25$ $11$ $13$ $7$ $12$ $31$ $19$ $10$ $12$ $17$ $18$ $11$ $32$ $17$ $16$ $2$ $7$ $9$ $7$ $8$ $3$ $5$ $12$ $15$ $18$ $3$ $12$ $14$ $2$ $9$ $6$ $15$ $15$ $7$ $6$ $12$
What is the empirical probability that an engineer lives:
$(i)$ less than $7 \, km$ from her place of work?
$(ii)$ more than or equal to $7 \, km$ from her place of work?
$(iii)$ 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:
$(i)$ less than $7 \, km$ from her place of work?
$(ii)$ more than or equal to $7 \, km$ from her place of work?
$(iii)$ within $\frac{1}{2} \, km$ from her place of work?
Medium
View SolutionFifty seeds were selected at random from each of $5$ bags of seeds,and were kept under standardised conditions favourable to germination. After $20$ days,the number of seeds which had germinated in each collection were counted and recorded as follows:
Bag $1$ $2$ $3$ $4$ $5$ Number of seeds germinated $40$ $48$ $42$ $39$ $41$
What is the probability of germination of
$(i)$ more than $40$ seeds in a bag?
$(ii)$ $49$ seeds in a bag?
$(iii)$ more than $35$ seeds in a bag?
| Bag | $1$ | $2$ | $3$ | $4$ | $5$ |
| Number of seeds germinated | $40$ | $48$ | $42$ | $39$ | $41$ |
What is the probability of germination of
$(i)$ more than $40$ seeds in a bag?
$(ii)$ $49$ seeds in a bag?
$(iii)$ more than $35$ seeds in a bag?
Medium
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