Three 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.
- A$\frac{90}{25}$
- B$\frac{9}{25}$
- C$\frac{9}{29}$
- D$\frac{19}{25}$
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$1500$ families with $2$ children were selected randomly,and the following data were recorded:
Number of girls in a family $2$ $1$ $0$ Number of families $475$ $814$ $211$
Compute the probability of a family,chosen at random,having:
$(i)$ $2$ girls $(ii)$ $1$ girl $(iii)$ No girl
Also,check whether the sum of these probabilities is $1$.
| Number of girls in a family | $2$ | $1$ | $0$ |
| Number of families | $475$ | $814$ | $211$ |
Compute the probability of a family,chosen at random,having:
$(i)$ $2$ girls $(ii)$ $1$ girl $(iii)$ No girl
Also,check whether the sum of these probabilities is $1$.
Difficult
View SolutionTo 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.
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 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 SolutionConsider the frequency distribution table which gives the weights of $38$ students of a class.
Weights (in $kg$) Number of students $31-35$ $9$ $36-40$ $5$ $41-45$ $14$ $46-50$ $3$ $51-55$ $1$ $56-60$ $2$ $61-65$ $2$ $66-70$ $1$ $71-75$ $1$ Total $38$
$(i)$ Find the probability that the weight of a student in the class lies in the interval $46-50 \, kg$.
$(ii)$ Give two events in this context,one having probability $0$ and the other having probability $1$.
| Weights (in $kg$) | Number of students |
| $31-35$ | $9$ |
| $36-40$ | $5$ |
| $41-45$ | $14$ |
| $46-50$ | $3$ |
| $51-55$ | $1$ |
| $56-60$ | $2$ |
| $61-65$ | $2$ |
| $66-70$ | $1$ |
| $71-75$ | $1$ |
| Total | $38$ |
$(i)$ Find the probability that the weight of a student in the class lies in the interval $46-50 \, kg$.
$(ii)$ Give two events in this context,one having probability $0$ and the other having probability $1$.
Medium
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