Advertisements
Advertisements
प्रश्न
If A and B are two independent events such that P (A ∪ B) = 0.60 and P (A) = 0.2, find P(B).
उत्तर
\[P\left( A \cup B \right) = P \left( A \right) + P\left( B \right) - P\left( A \cap B \right)\]
\[P\left( A \cup B \right) = P \left( A \right) + P\left( B \right) - P \left( A \right) \times P\left( B \right) \left[ \because \text{ A and B are independent events } \right]\]
\[ \Rightarrow 0 . 6 = 0 . 2 + P\left( B \right) - 0 . 2 \times P\left( B \right)\]
\[ \Rightarrow 0 . 6 - 0 . 2 = P\left( B \right)\left( 1 - 0 . 2 \right)\]
\[ \Rightarrow P\left( B \right) = \frac{0 . 6 - 0 . 2}{1 - 0 . 2}\]
\[ \Rightarrow P\left( B \right) = \frac{0 . 4}{0 . 8}\]
\[ \Rightarrow P\left( B \right) = \frac{1}{2}\]
\[ \Rightarrow P\left( B \right) = 0 . 5\]
APPEARS IN
संबंधित प्रश्न
In a set of 10 coins, 2 coins are with heads on both the sides. A coin is selected at random from this set and tossed five times. If all the five times, the result was heads, find the probability that the selected coin had heads on both the sides.
A couple has two children. Find the probability that both the children are (i) males, if it is known that at least one of the children is male. (ii) females, if it is known that the elder child is a female.
From a pack of 52 cards, two are drawn one by one without replacement. Find the probability that both of them are kings.
If P (A) = \[\frac{7}{13}\], P (B) = \[\frac{9}{13}\] and P (A ∩ B) = \[\frac{4}{13}\], find P (A/B).
If A and B are two events such that \[ P\left( A \right) = \frac{7}{13}, P\left( B \right) = \frac{9}{13} \text{ and } P\left( A \cap B \right) = \frac{4}{13}, \text{ then find } P\left( \overline{ A }|B \right) . \]
A pair of dice is thrown. Find the probability of getting 7 as the sum if it is known that the second die always exhibits a prime number.
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?
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 number of heads is odd, B = the number of tails is odd.
A card is drawn from a pack of 52 cards so the teach card is equally likely to be selected. In which of the following cases are the events A and B independent?
A = the card drawn is black, B = the card drawn is a king.
If A and B are two independent events such that P (`bar A` ∩ B) = 2/15 and P (A ∩`bar B` ) = 1/6, then find P (B).
A die is tossed twice. Find the probability of getting a number greater than 3 on each toss.
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.
An urn contains 4 red and 7 black balls. Two balls are drawn at random with replacement. Find the probability of getting 2 red balls.
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
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 - 2p1p2
A bag contains 3 white, 4 red and 5 black balls. Two balls are drawn one after the other, without replacement. What is the probability that one is white and the other is black?
A bag contains 8 red and 6 green balls. Three balls are drawn one after another without replacement. Find the probability that at least two balls drawn are green.
In a family, the husband tells a lie in 30% cases and the wife in 35% cases. Find the probability that both contradict each other on the same fact.
A husband and wife appear in an interview for two vacancies for the same post. The probability of husband's selection is 1/7 and that of wife's selection is 1/5. What is the probability that both of them will be selected ?
A husband and wife appear in an interview for two vacancies for the same post. The probability of husband's selection is 1/7 and that of wife's selection is 1/5. What is the probability that only one of them will be selected ?
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?
An urn contains 7 red and 4 blue balls. Two balls are drawn at random with replacement. Find the probability of getting
(i) 2 red balls
(ii) 2 blue balls
(iii) One red and one blue ball.
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?
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 four digit number is formed using the digits 1, 2, 3, 5 with no repetitions. Write the probability that the number is divisible by 5.
Three digit numbers are formed with the digits 0, 2, 4, 6 and 8. Write the probability of forming a three digit number with the same digits.
If A and B are two events write the expression for the probability of occurrence of exactly one of two events.
If P (A) = 0.3, P (B) = 0.6, P (B/A) = 0.5, find P (A ∪ B).
If A and B are independent events, then write expression for P(exactly one of A, B occurs).
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
Three faces of an ordinary dice are yellow, two faces are red and one face is blue. The dice is rolled 3 times. The probability that yellow red and blue face appear in the first second and third throws respectively, 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
Choose the correct alternative in the following question:
Associated to a random experiment two events A and B are such that
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
Mark the correct alternative in the following question:
Assume that in a family, each child is equally likely to be a boy or a girl. A family with three children is chosen at random. The probability that the eldest child is a girl given that the family has at least one girl is
