Advertisements
Advertisements
प्रश्न
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.
उत्तर
\[S = \left[ \left( H H H \right) \left( H H T \right) \left( H T H \right) \left( H T T \right) \left( T H H \right) \left( T H T \right) \left( T T H \right) \left( T T T \right) \right]\]
\[P\left( A \right) = \frac{4}{8} = \frac{1}{2}\]
\[P\left( B \right) = \frac{4}{8} = \frac{1}{2}\]
\[\text{ Now } , \]
\[P\left( A \cap B \right) = \frac{2}{8} = \frac{1}{4}\]
\[ P\left( A \cap B \right) = P\left( A \right)P\left( B \right)\]
\[\text{ Thus, A and B are independent events. } \]
APPEARS IN
संबंधित प्रश्न
Bag A contains 3 red and 5 black balls, while bag B contains 4 red and 4 black balls. Two balls are transferred at random from bag A to bag B and then a ball is drawn from bag B at random. If the ball drawn from bag B is found to be red find the probability that two red balls were transferred from A to B.
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 A and B are two events such that P (A) = \[\frac{1}{3},\] P (B) = \[\frac{1}{5}\] and P (A ∪ B) = \[\frac{11}{30}\] , find P (A/B) and P (B/A).
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.
A bag contains 20 tickets, numbered from 1 to 20. Two tickets are drawn without replacement. What is the probability that the first ticket has an even number and the second an odd number.
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 P (A) = \[\frac{7}{13}\], P (B) = \[\frac{9}{13}\] and P (A ∩ B) = \[\frac{4}{13}\], find P (A/B).
A coin is tossed three times. Find P (A/B) in each of the following:
A = At least two heads, B = At most two heads
A pair of dice is thrown. Find the probability of getting the sum 8 or more, if 4 appears on the first die.
Two dice are thrown and it is known that the first die shows a 6. Find the probability that the sum of the numbers showing on two dice is 7.
Given two independent events A and B such that P (A) = 0.3 and P (B) = `0.6. Find P (A ∩ overlineB ) `.
Given two independent events A and B such that P (A) = 0.3 and P (B) `= 0.6. Find P ( overlineA ∩ B) .`
Given two independent events A and B such that P (A) = 0.3 and P (B) = 0.6. Find P (A ∪ B).
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).
Three cards are drawn with replacement from a well shuffled pack of cards. Find the probability that the cards drawn are king, queen and jack.
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.
Two cards are drawn successively without replacement from a well-shuffled deck of 52 cards. Find the probability of exactly one ace.
A bag contains 4 red and 5 black balls, a second bag contains 3 red and 7 black balls. One ball is drawn at random from each bag, find the probability that the (i) balls are of different colours (ii) balls are of the same colour.
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.
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?
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?
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.
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.
If P (A) = 0.3, P (B) = 0.6, P (B/A) = 0.5, find P (A ∪ B).
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 speaks truth in 75% cases and B speaks truth in 80% cases. Probability that they contradict each other in a statement, 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
If A and B are two events, then P (`overline A` ∩ B) =
Mark the correct alternative in the following question:
\[\text{ If } P\left( B \right) = \frac{3}{5}, P\left( A|B \right) = \frac{1}{2} \text{ and } P\left( A \cup B \right) = \frac{4}{5}, \text{ then } P\left( B|\overline{ A } \right) = \]
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
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
If two events A and B are such that P (A)
\[\left( \overline{ A } \right)\] = 0.3, P (B) = 0.4 and P (A ∩ B) = 0.5, find P \[\left( B/\overline{ A }\cap \overline{ B } \right)\].
Out of 8 outstanding students of a school, in which there are 3 boys and 5 girls, a team of 4 students is to be selected for a quiz competition. Find the probability that 2 boys and 2 girls are selected.
Refer to Question 6. Calculate the probability that the defective tube was produced on machine E1.
