Addition Theorem of Probability for 3 Events

Q.

For the three events A, B and C, P (exactly one of the events A or B occurs) = P(exactly one of the events B or C occurs) = P(exactly one of the events C or A occurs) $=p$ and P (all the three events occur simultaneously) = $p^2$, where $0<p<\frac{1}{2}$. Then the probability of at least one of the three events A, B and C occurring is

1. $\frac{(3p+2p^2)}{2}$

2. $\frac{(p+3p^2)}{4}$

3. $\frac{(p+3p^2)}{2}$

4. $\frac{(3p+2p^2)}{4}$

Q. There are three persons A, B and C having different ages. The probability that A survives another 5 years is 0.80, B survives another 5 years is 0.60 and C survives another 5 years is 0.50. The probabilities that A and B survive another 5 years is 0.46, B and C survive another 5 years is 0.32 and A and C survive another 5 years 0.48. The probability that all these three persons survive another 5 years is 0.26. Find the probability that at least one of them survives another 5 years.

1. 0.8
2. 0.9
3. 0.25
4. 0.5

Q.

Suppose that a family has $5$ children. Also, suppose that the probability of having a girl is $\frac{1}{2}$. Find the probabilities that the family has the following children.
Exactly $3$ girls and $2$ boys

Q. A card is drawn from a pack of 52 cards. Find the probability of getting a king or a heart or a red card.
$\left[3\right]$

Q. A bag contains 3 white, 3 black and 2 red balls. One by one, three balls are drawn without replacing them. The probability that the third ball is red, is given by:

1. $\frac{5}{25}$
2. $\frac{1}{12}$
3. $\frac{1}{4}$
4. $None$

Q.

For the three events A, B and C, P (exactly one of the events A or B occurs) = P(exactly one of the events B or C occurs) = P(exactly one of the events C or A occurs)=p and P(all the three events occur simultaneously)=$p^2$, where 0<p<1/2. Then the probability of at least one of the three events A, B and C occuring is

1. $\frac{3p+2p^2}{2}$
   

2. $\frac{p+3p^2}{4}$
   

3. $\frac{p+3p^2}{2}$
   

4. $\frac{3p+2p^2}{4}$

Q. In a certain city only two newspapers A and B are published, it is known that 25% of the city population reads A and 20% reads B, while 8% reads both A and B. It is also known that 30% of those who read A but not B look into advertisements and 40% of those who read B but not A look into advertisements while 50% of those who read both A and B look into advertisements. If a person is chosen at random from the population, what is the percentage probability that he/she reads advertisements?

1. $\frac{139}{1000}$
2. $\frac{77}{250}$
3. $\frac{481}{2000}$
4. $\frac{61}{500}$