Calculating Probability for Complement of an Event

Q. If probability of an event is denoted by $P\left(E\right)$, then the probability of its complement is denoted by $P\left(\overline{E}\right)$.

1. True
2. False

Q. A spinner has 4 equal sectors colored yellow, blue, green, and red. What is the probability of landing on a sector that is not red after spinning this spinner?

1. $\frac{1}{4}$
2. $\frac{2}{4}$
3. $1$
4. $\frac{3}{4}$

Q.

If the probability that an event will happen is $0.2$, what is the probability of the events complement?

Q.

Two dice are thrown $400$ times. Each time sum of two numbers appearing on their tops is noted as given in the following table:

Sum	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$	$12$
Frequency	$14$	$20$	$32$	$45$	$62$	$65$	$60$	$43$	$36$	$18$	$5$

What is the probability of getting a sum (i) $5$, (ii) more than $10$, (iii) between $5and10$?

Q. Complement of an event is the occurrence of all the outcomes that are not favorable.

1. True
2. False

Q. If $P\left(\overline{E}\right)=\frac{9}{73}$, then find the value of $2\times P\left(E\right)$.

1. $\frac{66}{73}$
2. $\frac{132}{73}$
3. $\frac{73}{66}$
4. $\frac{73}{132}$

Q. In a school, there are 120 students. 20 students have no pets, 46 have only 1 pet, 33 have 2 pets, and 21 have at least 3 pets. If a student is picked at random, what is the probability that the student has at least 1 pet?

1. $\frac{1}{6}$
2. $\frac{2}{6}$
3. $\frac{4}{6}$
4. $\frac{5}{6}$

Q. If the probability of getting $5$ on a fair dice is $\frac{1}{6}$, then what would be the value of sum of Probability of getting $5$ and Probability of not getting $5$?

1. $\frac{2}{6}$
2. $\frac{1}{6}$
3. $1$
4. $\frac{5}{6}$

Q. A fair die is thrown. What is the probability of not rolling a factor of $5?$

1. $\frac{2}{3}$
2. $\frac{1}{3}$
3. $\frac{5}{6}$
4. $\frac{1}{6}$

Q. If the probability of an event $E$ is $\frac{7}{16}$, then what is the probability of complement of the event $E?$

1. $\frac{7}{16}$
2. $\frac{9}{16}$
3. $\frac{11}{16}$
4. $\frac{11}{16}$

Q. Jacob has a habit of oversleeping in the morning and when he oversleeps, he misses his breakfast. The probability of him oversleeping is $0.4$. What is the probability that he eats breakfast?

1. $0.4$
2. $1$
3. $0.6$
4. $0.1$

Q. Getting $1,2,3,5$ or $6$ on a fair dice is the same as not getting
on the fair dice.

Q. The complement of an event $A$ is represented by

1. $\overline{A}$
2. $A^2$
3. $-A$
4. None of the above

Q. A card is chosen at random from a standard deck of $52$ playing cards. What is the probability (in percent) of choosing a card that is not a club?

1. $55\%$
2. $65\%$
3. $70\%$
4. $75\%$

Q.

Use the numbers $0,\frac{1}{4},\frac{1}{2},\frac{2}{3}$ or $1$ to show what you think the probability is you will live until your ${160}^{th}$ birthday.