Fifty 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?
(A-D) The total number of bags is $5$.
$(i)$ The number of bags in which more than $40$ seeds germinated is $3$ (Bags $2, 3,$ and $5$).
Probability $= \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{3}{5} = 0.6$.
$(ii)$ The number of bags in which $49$ seeds germinated is $0$.
Probability $= \frac{0}{5} = 0$.
$(iii)$ The number of bags in which more than $35$ seeds germinated is $5$ (All bags).
Probability $= \frac{5}{5} = 1$.
$(i)$ The number of bags in which more than $40$ seeds germinated is $3$ (Bags $2, 3,$ and $5$).
Probability $= \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{3}{5} = 0.6$.
$(ii)$ The number of bags in which $49$ seeds germinated is $0$.
Probability $= \frac{0}{5} = 0$.
$(iii)$ The number of bags in which more than $35$ seeds germinated is $5$ (All bags).
Probability $= \frac{5}{5} = 1$.
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Similar Questions
The following frequency distribution table shows the concentration of sulphur dioxide $(SO_2)$ in the air in parts per million $(ppm)$ of a certain city for $30$ days. Using this table,find the probability of the concentration of sulphur dioxide being in the interval $0.12 - 0.16$ on any of these days.
Concentration of $SO_2$ (in $ppm$) Number of days (frequency) $0.00-0.04$ $4$ $0.04-0.08$ $9$ $0.08-0.12$ $9$ $0.12-0.16$ $2$ $0.16-0.20$ $4$ $0.20-0.24$ $2$ Total $30$
| Concentration of $SO_2$ (in $ppm$) | Number of days (frequency) |
| $0.00-0.04$ | $4$ |
| $0.04-0.08$ | $9$ |
| $0.08-0.12$ | $9$ |
| $0.12-0.16$ | $2$ |
| $0.16-0.20$ | $4$ |
| $0.20-0.24$ | $2$ |
| Total | $30$ |
Medium
View SolutionEleven bags of wheat flour,each marked $5 \,kg$,actually contained the following weights of flour (in $kg$):
$4.97, 5.05, 5.08, 5.03, 5.00, 5.06, 5.08, 4.98, 5.04, 5.07, 5.00$
Find the probability that any of these bags chosen at random contains more than $5 \,kg$ of flour.
$4.97, 5.05, 5.08, 5.03, 5.00, 5.06, 5.08, 4.98, 5.04, 5.07, 5.00$
Find the probability that any of these bags chosen at random contains more than $5 \,kg$ of flour.
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 SolutionThe 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 SolutionThe percentage of marks obtained by a student in the monthly unit tests are given below:
Unit test $I$ $II$ $III$ $IV$ $V$ Percentage of marks obtained $69$ $71$ $73$ $68$ $74$
Based on this data,find the probability that the student gets more than $70\%$ marks in a unit test.
| Unit test | $I$ | $II$ | $III$ | $IV$ | $V$ |
| Percentage of marks obtained | $69$ | $71$ | $73$ | $68$ | $74$ |
Based on this data,find the probability that the student gets more than $70\%$ marks in a unit test.
Medium
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