Advertisements
Advertisements
प्रश्न
Mark the correct alternative in the following question: A bag contains 5 red and 3 blue balls. If 3 balls are drawn at random without replacement, then the probability of getting exactly one red ball is
विकल्प
\[ \frac{15}{29}\]
\[\frac{15}{56} \]
\[ \frac{45}{196} \]
\[ \frac{135}{392}\]
उत्तर
\[\text{ We have } , \]
\[\text{ The number of red balls = 5 and } \]
\[\text{ The number of blue balls = 3} \]
\[\text{ Let R be the event of getting a red ball and} \]
\[ \text{ B be the event of getting a blue ball .} \]
\[\text{ Now } , \]
\[P\left( \text{ Getting exactly one red ball } \right) = P\left( RBB \right) + P\left( BRB \right) + P\left( BBR \right)\]
\[ = P\left( R \right) \times P\left( B|R \right) \times P\left( B|RB \right) + P\left( B \right) \times P\left( R|B \right) \times P\left( B|BR \right) + P\left( B \right) \times P\left( B|B \right) \times P\left( R|BB \right)\]
\[ = \frac{5}{8} \times \frac{3}{7} \times \frac{2}{6} + \frac{3}{8} \times \frac{5}{7} \times \frac{2}{6} + \frac{3}{8} \times \frac{2}{7} \times \frac{5}{6}\]
\[ = \frac{5}{56} + \frac{5}{56} + \frac{5}{56}\]
\[ = \frac{15}{56}\]
APPEARS IN
संबंधित प्रश्न
Ten cards numbered 1 through 10 are placed in a box, mixed up thoroughly and then one card is drawn randomly. If it is known that the number on the drawn card is more than 3, what is the probability that it is an even number?
Given that the two numbers appearing on throwing two dice are different. Find the probability of the event 'the sum of numbers on the dice is 4'.
If P (A) = 0.4, P (B) = 0.3 and P (B/A) = 0.5, find P (A ∩ B) and P (A/B).
Find the chance of drawing 2 white balls in succession from a bag containing 5 red and 7 white balls, the ball first drawn not being replaced.
A bag contains 25 tickets, numbered from 1 to 25. A ticket is drawn and then another ticket is drawn without replacement. Find the probability that both tickets will show even numbers.
Two cards are drawn without replacement from a pack of 52 cards. Find the probability that both are kings .
If A and B are two events such that 2 P (A) = P (B) = \[\frac{5}{13}\] and P (A/B) = \[\frac{2}{5},\] find P (A ∪ B).
Two coins are tossed once. Find P (A/B) in each of the following:
A = No tail appears, B = No head appears.
A die is thrown twice and the sum of the numbers appearing is observed to be 8. What is the conditional probability that the number 5 has appeared at least once?
A coin is tossed thrice and all the eight outcomes are assumed equally likely. In which of the following cases are the following events A and B are independent?
A = the first throw results in head, B = the last throw results in tail.
Prove that in throwing a pair of dice, the occurrence of the number 4 on the first die is independent of the occurrence of 5 on the second die.
Given two independent events A and B such that P (A) = 0.3 and P (B) = 0.6. Find P (A ∩ B).
An article manufactured by a company consists of two parts X and Y. In the process of manufacture of the part X, 9 out of 100 parts may be defective. Similarly, 5 out of 100 are likely to be defective in the manufacture of part Y. Calculate the probability that the assembled product will not be defective.
The odds against a certain event are 5 to 2 and the odds in favour of another event, independent to the former are 6 to 5. Find the probability that (i) at least one of the events will occur, and (ii) none of the events will occur.
An urn contains 4 red and 7 black balls. Two balls are drawn at random with replacement. Find the probability of getting one red and one blue ball.
Let A and B be two independent events such that P(A) = p1 and P(B) = p2. Describe in words the events whose probabilities are: p1 p2 .
Let A and B be two independent events such that P(A) = p1 and P(B) = p2. Describe in words the events whose probabilities are: (1 - p1)p2
A bag contains 7 white, 5 black and 4 red balls. Four balls are drawn without replacement. Find the probability that at least three balls are black.
A bag contains 4 white, 7 black and 5 red balls. 4 balls are drawn with replacement. What is the probability that at least two are white?
Three cards are drawn with replacement from a well shuffled pack of 52 cards. Find the probability that the cards are a king, a queen and a jack.
A purse contains 2 silver and 4 copper coins. A second purse contains 4 silver and 3 copper coins. If a coin is pulled at random from one of the two purses, what is the probability that it is a silver coin?
A bag contains 3 white and 2 black balls and another bag contains 2 white and 4 black balls. One bag is chosen at random. From the selected bag, one ball is drawn. Find the probability that the ball drawn is white.
An unbiased coin is tossed. If the result is a head, a pair of unbiased dice is rolled and the sum of the numbers obtained is noted. If the result is a tail, a card from a well shuffled pack of eleven cards numbered 2, 3, 4, ..., 12 is picked and the number on the card is noted. What is the probability that the noted number is either 7 or 8?
A bag contains 4 white and 5 black balls and another bag contains 3 white and 4 black balls. A ball is taken out from the first bag and without seeing its colour is put in the second bag. A ball is taken out from the latter. Find the probability that the ball drawn is white.
One bag contains 4 white and 5 black balls. Another bag contains 6 white and 7 black balls. A ball is transferred from first bag to the second bag and then a ball is drawn from the second bag. Find the probability that the ball drawn is white.
A bag contains 6 red and 8 black balls and another bag contains 8 red and 6 black balls. A ball is drawn from the first bag and without noticing its colour is put in the second bag. A ball is drawn from the second bag. Find the probability that the ball drawn is red in colour.
Three numbers are chosen from 1 to 20. Find the probability that they are consecutive.
If A and B are independent events, then write expression for P(exactly one of A, B occurs).
Three integers are chosen at random from the first 20 integers. The probability that their product is even is
Two dice are thrown simultaneously. The probability of getting a pair of aces is
A box contains 10 good articles and 6 with defects. One item is drawn at random. The probability that it is either good or has a defect is
Mark the correct alternative in the following question:
\[\text{ If A and B are two events such that } P\left( A \right) = \frac{1}{2}, P\left( B \right) = \frac{1}{3}, P\left( A|B \right) = \frac{1}{4}, \text{ then } P\left( A \cap B \right) \text{ equals} \]
Mark the correct alternative in the following question:
\[\text{ If} P\left( A \right) = 0 . 4, P\left( B \right) = 0 . 8 \text{ and } P\left( B|A \right) = 0 . 6, \text{ then } P\left( A \cup B \right) = \]
Mark the correct alternative in the following question
Three persons, A, B and C fire a target in turn starting with A. Their probabilities of hitting the target are 0.4, 0.2 and 0.2, respectively. The probability of two hits is
A and B are two students. Their chances of solving a problem correctly are `1/3` and `1/4` respectively. If the probability of their making common error is `1/20` and they obtain the same answer, then the probability of their answer to be correct is
