Advertisements
Advertisements
प्रश्न
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.
उत्तर
\[\text{ The odds against event A are 5 to 2. } \]
\[P\left( A \right) = \frac{2}{5 + 2} = \frac{2}{7}\]
\[\text{ The oddsin favour of event B are 6 to 5 } .\]
\[P\left( B \right) = \frac{6}{6 + 5} = \frac{6}{11}\]
\[\left( i \right) P\left( \text{ atleast one event occurs } \right)\]
\[ = P\left( A \cup B \right)\]
\[ = P\left( A \right) + P\left( B \right) - P\left( A \cap B \right)\]
\[ = P\left( A \right) + P\left( B \right) - P\left( A \right) \times P\left( B \right)\]
\[ = \frac{2}{7} + \frac{6}{11} - \frac{2}{7} \times \frac{6}{11}\]
\[ = \frac{22 + 42}{77} - \frac{12}{77}\]
\[ = \frac{22 + 42 - 12}{77} = \frac{52}{77}\]
\[ \therefore P\left( A \cup B \right) = \frac{52}{77}\]
\[\left( ii \right) P\left( \text{ none of the event occurs } \right)\]
\[ = 1 - P\left( A \cup B \right)\]
\[ = 1 - \frac{52}{77}\]
\[ = \frac{25}{77}\]
APPEARS IN
संबंधित प्रश्न
A and B throw a pair of dice alternately, till one of them gets a total of 10 and wins the game. Find their respective probabilities of winning, if A starts first
How many times must a fair coin be tossed so that the probability of getting at least one head is more than 80%?
A and B throw a pair of dice alternately. A wins the game if he gets a total of 7 and B wins the game if he gets a total of 10. If A starts the game, then find the probability that B wins
A bag A contains 4 black and 6 red balls and bag B contains 7 black and 3 red balls. A die is thrown. If 1 or 2 appears on it, then bag A is chosen, otherwise bag B, If two balls are drawn at random (without replacement) from the selected bag, find the probability of one of them being red and another black.
From a pack of 52 cards, two are drawn one by one without replacement. Find the probability that both of them are kings.
From a deck of cards, three cards are drawn on by one without replacement. Find the probability that each time it is a card of spade.
Two cards are drawn without replacement from a pack of 52 cards. Find the probability that both are kings .
An urn contains 10 black and 5 white balls. Two balls are drawn from the urn one after the other without replacement. What is the probability that both drawn balls are black?
If A and B are two events such that \[ P\left( A \right) = \frac{1}{3}, P\left( B \right) = \frac{1}{4} \text{ and } P\left( A \cup B \right) = \frac{5}{12}, \text{ then find } P\left( A|B \right) \text{ and } P\left( B|A \right) . \]
If A and B are two events such that
\[ P\left( A \right) = \frac{1}{2}, P\left( B \right) = \frac{1}{3} \text{ and } P\left( A \cap B \right) = \frac{1}{4}, \text{ then find } P\left( A|B \right), P\left( B|A \right), P\left( \overline{ A }|B \right) \text{ and } P\left( \overline{ A }|\overline{ B } \right) .\]
If P (A) = \[\frac{6}{11},\] P (B) = \[\frac{5}{11}\] and P (A ∪ B) = \[\frac{7}{11},\] find
Two coins are tossed once. Find P (A/B) in each of the following:
A = Tail appears on one coin, B = One coin shows head.
Mother, father and son line up at random for a family picture. If A and B are two events given by A = Son on one end, B = Father in the middle, find P (A/B) and P (B/A).
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 an odd 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 first throw results in head, B = the last throw results in tail.
A coin is tossed three times. Let the events A, B and C be defined as follows:
A = first toss is head, B = second toss is head, and C = exactly two heads are tossed in a row.
Check the independence of A and B.
A coin is tossed three times. Let the events A, B and C be defined as follows:
A = first toss is head, B = second toss is head, and C = exactly two heads are tossed in a row. B and C .
A coin is tossed three times. Let the events A, B and C be defined as follows:
A = first toss is head, B = second toss is head, and C = exactly two heads are tossed in a row. C and A
A and B are two independent events. The probability that A and B occur is 1/6 and the probability that neither of them occurs is 1/3. Find the probability of occurrence of two events.
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.
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.
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 none of them will be selected?
There are 3 red and 5 black balls in bag 'A'; and 2 red and 3 black balls in bag 'B'. One ball is drawn from bag 'A' and two from bag 'B'. Find the probability that out of the 3 balls drawn one is red and 2 are black.
Fatima and John appear in an interview for two vacancies for the same post. The probability of Fatima's selection is \[\frac{1}{7}\] and that of John's selection is \[\frac{1}{5}\] What is the probability that
(i) both of them will be selected?
(ii) only one of them will be selected?
(iii) none of them will be selected?
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.
A and B throw a pair of dice alternately. A wins the game if he gets a total of 7 and B wins the game if he gets a total of 10. If A starts the game, then find the probability that B wins.
One bag contains 4 yellow and 5 red balls. Another bag contains 6 yellow and 3 red balls. A ball is transferred from the first bag to the second bag and then a ball is drawn from the second bag. Find the probability that ball drawn is yellow.
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.
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.
A ordinary cube has four plane faces, one face marked 2 and another face marked 3, find the probability of getting a total of 7 in 5 throws.
If A and B are two independent events such that P (A) = 0.3 and P (A ∪ \[B\]) = 0.8. Find P (B).
In a competition A, B and C are participating. The probability that A wins is twice that of B, the probability that B wins is twice that of C. Find the probability that A losses.
If A and B are two events, then P (`overline A` ∩ B) =
A bag X contains 2 white and 3 black balls and another bag Y contains 4 white and 2 black balls. One bag is selected at random and a ball is drawn from it. Then, the probability chosen to be white 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:
In a college 30% students fail in Physics, 25% fail in Mathematics and 10% fail in both. One student is chosen at random. The probability that she fails in Physics if she failed in Mathematics 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
