# Independent Events

## Trending Questions

**Q.**state and prove addition therom of probability

**Q.**

Two dice are tossed once. The probability of getting an even number at the first dice or a total of $8$ is

$\frac{1}{36}$

$\frac{3}{36}$

$\frac{11}{36}$

$\frac{5}{9}$

**Q.**

How do you find the probability of three Independent events $?$

**Q.**The probabilities that a student passes in Mathematics, Physics and Chemistry are m, p and c respectively. On these subjects, the student has a 75% chance of passing in at least one, a 50% chance of passing in at least two and a 40% chance of passing in exactly two. Which of the following relations are true.

**Q.**

If $P\left(A\right)=0.4,P\left(B\right)=x,P\left(AUB\right)=0.7$, and the events $A$ and $B$ are mutually exclusive, then$x=?$

$\frac{3}{10}$

$\frac{1}{2}$

$\frac{2}{5}$

$\frac{1}{5}$

**Q.**A real estate man has eight master keys to open several new homes. Only one master key will open any given home. If 40% of these homes are usually left unlocked, the probability that the real estate man can get into a specific home, if it is given that he selected 3 keys randomly before leaving his office, is equal to:

- 58
- 38
- 34
- 940

**Q.**

A purse contains $4$ copper coins and $3$ silver coins, the second purse contains $6$ copper coins and $2$ silver coins. If a coin is drawn out of any purse, then the probability that it is a copper coin is

$\frac{4}{7}$

$\frac{3}{4}$

$\frac{37}{56}$

None of these

**Q.**

The probability of happening an event $A$ is one trial is $0.4$. The probability that the event $A$ happens at least once in three independent trials is

$0.936$

$0.784$

$0.904$

$0.216$

**Q.**The probability that a randomly selected 2-digit number belongs to the set {n ϵ N: (2n−2) is a multiple of 3} is equal to

**Q.**Suppose you have a box with 3 blue marbles, 2 red marbles, and 4 yellow marbles. You are going to pull out one marble, record its color, put it back in the box and draw another marble. What is the probability of pulling out a red marble followed by a blue marble?

- 881
- 227
- 127
- 19

**Q.**

Find the probability distribution of the number of successes in two tosses of a die, where a succeess is defined as

number greater than 4

six appears on the die.

**Q.**An electrical system has open-closed switches S

_{1}, S

_{2}and S

_{3}as shown in Figure.

The switches operate independently of one another and the current will flow from A and B either if S1 is closed or if both S2 and S3 are closed. If P(S1)=P(S2)=P(S3)=12, then find the probability that the circuit will work

**Q.**

The probability that $A$ speaks truth is $\frac{4}{5}$, while this probability for $B$ is $\frac{3}{4}$. The probability that they contradict each other when asked to speak on a fact

$\frac{4}{5}$

$\frac{1}{5}$

$\frac{7}{20}$

$\frac{3}{20}$

**Q.**

An ordinary cube has four blank faces, one face marked $2$ another marked $3$. Then the probability of obtaining a total of exactly $12$ in $5$ throws is

$\frac{5}{1296}$

$\frac{5}{1944}$

$\frac{5}{2592}$

None of these

**Q.**

The probability that a certain beginner at golf gets a good shot if he uses the correct club is $\frac{1}{3}$ and the probability of a good shot with an incorrect club is $\frac{1}{4}$. In his bag, there are $5$different clubs, only one of which is correct for the shot in question. If he chooses a club at random and takes a stroke, the probability that he gets a good shot is

$\frac{2}{3}$

$\frac{1}{15}$

$\frac{4}{15}$

$\frac{7}{15}$

**Q.**

How do you find the probability of $A$and $B$ $?$

**Q.**

Let E and F be two independent events. The probability that both E and F happen is 1/12 and the probability that neither E nor F happens is 1/2 .Then,

(a) P(E)=1/3, P(F)=1/4

(b) P(E)=1/2, P(F)=1/6

(c) P(E)=1/6, P(F)=1/2

(d) P(E)=1/12, P(F)=1

**Q.**An unbiased coin is tossed. If the outcome is head then a pair of unbiased dice is rolled and the sum of the numbers obtained on them is noted. If the toss of the coin results in tail then a card from a well shuffled pack of nine cards numbered 1, 2, ⋯9 is randomly picked and the number on the card is noted. The probability that the noted number is either 7 or 8 is :

- 1936
- 1572
- 1336
- 1972

**Q.**On a toss of two dice, A throws a total of 5. Then the probability that he will throw another 5 before he throws 7 is

- 245
- 25
- 181
- 19

**Q.**

There are 5% defective items in a large bulk of items. What is the probability that a sample of 10 items will include not more than one defective item?

**Q.**Two cards are drawn one by one without replacement from a pack of 52 cards. The probability that the second card is of higher rank than the first card is

(rank in increasing order can be taken from ace to king)

- 117
- 817
- 12
- 1617

**Q.**Two persons A, B speaks truth with probabilities 0.6 and 0.7 respectively. The probability that they will say the same thing while describing a single event is:

- 0.56
- 0.54
- 0.38
- 0.94

**Q.**

A box contains $15$ tickets numbered $1,2,...,15$. Seven tickets are drawn at random one after the other with replacement. The probability that the greatest number on a drawn ticket is $9$ is

${\left(\frac{9}{10}\right)}^{6}$

${\left(\frac{8}{15}\right)}^{7}$

${\left(\frac{3}{5}\right)}^{7}$

None of these

**Q.**

In an examination, the probability of a candidate solving a question is $\frac{1}{2}$. Out of given $5$ questions in the examination, what is the probability that the candidate was able to solve at least $2$ questions?

$\frac{1}{64}$

$\frac{3}{16}$

$\frac{1}{2}$

$\frac{13}{16}$

**Q.**

If four persons independently solve a certain problem correctly with the probabilities $\frac{1}{2},\frac{3}{4},\frac{1}{4}\mathrm{and}\frac{1}{8}$. Then, the probability that the problem is solved correctly by at least one of them is,

$\frac{235}{256}$

$\frac{21}{256}$

$\frac{3}{256}$

$\frac{253}{256}$

**Q.**A and B are independent events. The probability that both A and B occur is 120 and the probability that neither of them occurs is 35. The probability of occurence of A is

- 12
- 110
- 14
- 15

**Q.**A bag contains n white and n black balls. Pairs of balls are drawn without replacement until the bag is empty.The probability that each pair consists of one white and one black ball is

**Q.**

In a hurdle race, a player has to cross 10 hurdles. The probability that he will clear hurdles is 56. What is the probability that he will knock down fewer than 2 hurdles?

**Q.**A box contains N coins, m of which are fair and the rest are biased. The probability of getting a head when a fair coin is tossed is 12, while it is 23 when a biased coin is tossed. A coin is drawn from the box at random and is tossed twice. Then the probability that the coin drawn is fair, when first toss head, second toss tail is:

- 9m8N+m
- 9m8N−m
- 9m8m−N
- 9m8m+N

**Q.**

A die is thrown three times,

E: 4 appears on the third toss, F: 6 and 5 appears respectively on first two tosses