Addition Theorem of Probability for 2 Events

Q. Three coins are tossed simultaneously. What is the probability of getting exactly two heads?

1. $\frac{1}{2}$
2. $\frac{3}{8}$
3. $\frac{3}{4}$
4. $\frac{1}{4}$

Q. Two events A and B have the probabilities 0.25 and 0.5 respectively. The probability that both A and B simultaneously is 0.12. then the probability that neither A and nor B occurs is ___.

1. 0.13
2. 0.38
3. 0.63
4. 0.37

Q. A number is randomly selected from the first 40 natural numbers. What is the probability that the selected number is divisible by 5 or 7?

1. $\frac{8}{20}$
2. $\frac{17}{40}$
3. $\frac{7}{20}$
4. $\frac{3}{10}$

Q. A and B are two candidates for seeking admission in IIT. The probability that A is selected is 0.4 and the probability that both A and B are selected is at the most 0.2. Then P(B) is less than:

1. 0.9
2. 0.7
3. 0.8
4. None

Q. A single card is chosen at random from a standard deck of 52 playing cards. What is the probability that the card will be a club or a king?

1. $\frac{1}{4}$
2. $\frac{4}{13}$
3. $\frac{1}{13}$
4. $\frac{3}{13}$

Q. A number is selected from the first 25 natural numbers. What is the probability that it would be divisible by 4 or 7 ?

1. $\frac{1}{25}$
2. $\frac{9}{25}$
3. $\frac{9}{14}$
4. $\frac{6}{11}$

Q. Three natural numbers are taken at random from the set $A=\{x|1\le x\le 100,xϵN\}$. The probability that the AM of the numbers is $25$, is

1. $\frac{{}^{77}{C}_2}{{}^{100}{C}_3}$
2. $\frac{{}^{25}{C}_2}{{}^{100}{C}_3}$
3. $\frac{{}^{74}{C}_{72}}{{}^{100}{C}_{97}}$
4. none of these

Q. An unbiased cubic die marked with $1,2,2,3,3,3$ is rolled $3$ times. The probability of getting a total score of $4$ or $6$ is

1. $\frac{16}{216}$
2. $\frac{50}{216}$
3. $\frac{60}{216}$
4. none of these

Q. India play two matches each with West Indies and Australia. In any match the probabilities of India getting $0,1$ and $2$ points are $0.45,0.05$ and $0.50$ respectively. Assuming that the outcomes are independent, the probability of India getting at least $7$ points is

1. $0.0875$
2. $\frac{1}{16}$
3. $0.1125$
4. none of these

Q. In a factory manufacturing bolts; machines $A,B$ and $C$ manufacture respectively $20\%,30\%$ and $50\%$ of the total production. Of their outputs, $2\%,3\%$ and $5\%$ are defective bolts. A bolt is drawn at random from the product and is found to be defective. What is the probability that it was manufactured by machine $C$?