Advertisements
Advertisements
प्रश्न
If P (not B) = 0.65, P (A ∪ B) = 0.85, and A and B are independent events, then find P (A).
उत्तर
\[P\left( \bar{B} \right) = 0 . 65\]
\[ \Rightarrow 1 - P\left( B \right) = 0 . 65\]
\[ \Rightarrow P\left( B \right) = 1 - 0 . 65 = 0 . 35\]
\[\text{ Now } , \]
\[P\left( A \cup B \right) = P\left( A \right) + P\left( B \right) - P\left( A \cap B \right)\]
\[ \Rightarrow P\left( A \cup B \right) = P\left( A \right) + P\left( B \right) - P\left( A \right) \times P\left( B \right)\]
\[ \Rightarrow 0 . 85 = P\left( A \right) + 0 . 35 - 0 . 35 \times P\left( A \right)\]
\[ \Rightarrow 0 . 85 - 0 . 35 = P\left( A \right)\left[ 1 - 0 . 35 \right]\]
\[ \Rightarrow P\left( A \right) = \frac{0 . 5}{0 . 65} = 0 . 77\]
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.
An experiment succeeds thrice as often as it fails. Find the probability that in the next five trials, there will be at least 3 successes.
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.
If A and B are two events such that\[ P\left( A \right) = \frac{6}{11}, P\left( B \right) = \frac{5}{11} \text{ and } P\left( A \cup B \right) = \frac{7}{11}, \text{ then find } P\left( A \cap B \right), P\left( A|B \right) \text { and } P\left( B|A \right) . \]
A coin is tossed three times. Find P (A/B) in each of the following:
A = At most two tails, B = At least one tail.
A die is rolled. If the outcome is an odd number, what is the probability that it is prime?
A pair of dice is thrown. Let E be the event that the sum is greater than or equal to 10 and F be the event "5 appears on the first-die". Find P (E/F). If F is the event "5 appears on at least one die", find P (E/F).
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 two, B = the last throw results in head.
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).
A die is tossed twice. Find the probability of getting a number greater than 3 on each toss.
A die is thrown thrice. Find the probability of getting an odd number at least once.
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 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, B, and C are independent witness of an event which is known to have occurred. Aspeaks the truth three times out of four, B four times out of five and C five times out of six. What is the probability that the occurrence will be reported truthfully by majority of three witnesses?
A bag contains 4 white balls and 2 black balls. Another contains 3 white balls and 5 black balls. If one ball is drawn from each bag, find the probability that
(i) both are white
(ii) both are black
(iii) one is white and one is black
There are three urns A, B, and C. Urn A contains 4 red balls and 3 black balls. urn B contains 5 red balls and 4 black balls. Urn C contains 4 red and 4 black balls. One ball is drawn from each of these urns. What is the probability that 3 balls drawn consists of 2 red balls and a black ball?
A and B take turns in throwing two dice, the first to throw 9 being awarded the prize. Show that their chance of winning are in the ratio 9:8.
A bag contains 8 marbles of which 3 are blue and 5 are red. One marble is drawn at random, its colour is noted and the marble is replaced in the bag. A marble is again drawn from the bag and its colour is noted. Find the probability that the marble will be
(i) blue followed by red.
(ii) blue and red in any order.
(iii) of the same colour.
A bag A contains 5 white and 6 black balls. Another bag B contains 4 white and 3 black balls. A ball is transferred from bag A to the bag B and then a ball is taken out of the second bag. Find the probability of this ball being black.
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.
The contents of three bags I, II and III are as follows:
Bag I : 1 white, 2 black and 3 red balls,
Bag II : 2 white, 1 black and 1 red ball;
Bag III : 4 white, 5 black and 3 red balls.
A bag is chosen at random and two balls are drawn. What is the probability that the balls are white and red?
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.
If A, B and C are independent events such that P(A) = P(B) = P(C) = p, then find the probability of occurrence of at least two of A, B and C.
A and B are two events such that P (A) = 0.25 and P (B) = 0.50. The probability of both happening together is 0.14. The probability of both A and B not happening is
A bag contains 5 black balls, 4 white balls and 3 red balls. If a ball is selected randomwise, the probability that it is black or red ball is
Choose the correct alternative in the following question:
\[\text{ If } P\left( A \right) = \frac{2}{5}, P\left( B \right) = \frac{3}{10} \text{ and } P\left( A \cap B \right) = \frac{1}{5}, \text{ then } , P\left( \overline { A }|\overline{ B } \right) P\left( \overline{ B }|\overline{ A } \right) \text{ is equal to } \]
Mark the correct alternative in the following question:
\[ \text{ If } P\left( B \right) = \frac{3}{5}, P\left( A|B \right) = \frac{1}{2} \text{ and } P\left( \overline{A \cup B }\right) = \frac{4}{5}, \text{ then } P\left( \overline{ A } \cup B \right) + P\left( A \cup B \right) = \]
If A and B are two events such that A ≠ Φ, B = Φ, then
Mark the correct alternative in the following question:A flash light has 8 batteries out of which 3 are dead. If two batteries are selected without replacement and tested, then the probability that both are dead is
Mark the correct alternative in the following question:
Two cards are drawn from a well shuffled deck of 52 playing cards with replacement. The probability that both cards are queen is
Mark the correct alternative in the following question:
A box contains 3 orange balls, 3 green balls and 2 blue balls. Three balls are drawn at random from the box without replacement. The probability of drawing 2 green balls and one blue ball is
Mark the correct alternative in the following question:
\[\text{ Let A and B be two events . If } P\left( A \right) = 0 . 2, P\left( B \right) = 0 . 4, P\left( A \cup B \right) = 0 . 6, \text{ then } P\left( A|B \right) \text{ is equal to} \]
Mark the correct alternative in the following question:
\[\text{ Let A and B be two events such that P } \left( A \right) = 0 . 6, P\left( B \right) = 0 . 2, P\left( A|B \right) = 0 . 5 . \text{ Then } P\left( \overline{A}|\overline{B} \right) \text{ equals } \]
