State whether each of the following statements is true or false:
$(1)$ For the probability $P(A)$ of any event $A$,$0 < P(A) < 1$.
$(2)$ The probability of the month of March having $5$ Sundays is $\frac{1}{7}$.
$(3)$ If the probability of an event $A$ occurring is $\frac{3}{7}$,then the probability of event $A$ not occurring is $\frac{4}{7}$.
$(1)$ For the probability $P(A)$ of any event $A$,$0 < P(A) < 1$.
$(2)$ The probability of the month of March having $5$ Sundays is $\frac{1}{7}$.
$(3)$ If the probability of an event $A$ occurring is $\frac{3}{7}$,then the probability of event $A$ not occurring is $\frac{4}{7}$.
(C) $(1)$ False. The probability $P(A)$ of any event $A$ satisfies $0 \le P(A) \le 1$. It can be $0$ (impossible event) or $1$ (sure event).
$(2)$ False. March has $31$ days,which means $4$ weeks and $3$ extra days. The extra days can be (Sun,Mon,Tue),(Mon,Tue,Wed),(Tue,Wed,Thu),(Wed,Thu,Fri),(Thu,Fri,Sat),(Fri,Sat,Sun),or (Sat,Sun,Mon). Out of $7$ possibilities,$3$ contain a Sunday. Thus,the probability is $\frac{3}{7}$.
$(3)$ True. The probability of an event not occurring is $P(\text{not } A) = 1 - P(A)$. Given $P(A) = \frac{3}{7}$,then $P(\text{not } A) = 1 - \frac{3}{7} = \frac{4}{7}$.
$(2)$ False. March has $31$ days,which means $4$ weeks and $3$ extra days. The extra days can be (Sun,Mon,Tue),(Mon,Tue,Wed),(Tue,Wed,Thu),(Wed,Thu,Fri),(Thu,Fri,Sat),(Fri,Sat,Sun),or (Sat,Sun,Mon). Out of $7$ possibilities,$3$ contain a Sunday. Thus,the probability is $\frac{3}{7}$.
$(3)$ True. The probability of an event not occurring is $P(\text{not } A) = 1 - P(A)$. Given $P(A) = \frac{3}{7}$,then $P(\text{not } A) = 1 - \frac{3}{7} = \frac{4}{7}$.
Explore More
Similar Questions
$A$ box contains $100$ cards marked with numbers $1$ to $100$. If one card is drawn at random from the box,find the probability that the number on the card is: $(1)$ a multiple of $7$,$(2)$ a number smaller than $30$,$(3)$ a prime number.
Difficult
View Solution$A$ recent survey found that the ages of workers in a factory is distributed as follows:
Age (in years) $20-29$ $30-39$ $40-49$ $50-59$ $60$ and above Number of workers $38$ $27$ $86$ $46$ $3$
If a person is selected at random,find the probability that the person is under $40$ years.
| Age (in years) | $20-29$ | $30-39$ | $40-49$ | $50-59$ | $60$ and above |
| Number of workers | $38$ | $27$ | $86$ | $46$ | $3$ |
If a person is selected at random,find the probability that the person is under $40$ years.
Medium
View SolutionOn tossing two coins simultaneously,find the probability of getting no tail.
Medium
View Solution$A$ die is thrown $1000$ times and the outcomes were recorded as follows:
Outcome $1$ $2$ $3$ $4$ $5$ $6$ Frequency $180$ $150$ $160$ $170$ $150$ $190$
If the die is thrown once more,then the probability that it shows $5$ is:
| Outcome | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ |
| Frequency | $180$ | $150$ | $160$ | $170$ | $150$ | $190$ |
If the die is thrown once more,then the probability that it shows $5$ is:
Easy
View SolutionIn cricket,Rohit hits a century in $4$ innings out of $10$ innings. Find the probability that he did not hit a century.
Medium
View SolutionVedclass Products
For Students
Vedclass Test Series
Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.
Start Free TrialFor Teachers
Exam Paper Generator
Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.
Try FreeFor Institutes
Online Exam Module
Live online exams with unlimited students, 360° analytics & white-label branding.
See Demo