Advertisements
Advertisements
प्रश्न
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?
उत्तर
\[P\left( \text{ Fatima gets selected } \right) = P\left( A \right) = \frac{1}{7}\]
\[P\left( \text{ John gets selected } \right) = P\left( B \right) = \frac{1}{5}\]
\[\left( i \right) P\left( \text{ both of them get selected} \right) = P\left( A \cap B \right)\]
\[ = P\left( A \right) \times P\left( B \right)\]
\[ = \frac{1}{7} \times \frac{1}{5} = \frac{1}{35}\]
\[\left( ii \right) P\left( \text{ only one of them gets selected } \right) = P\left( A \right) \times P\left( \bar{B} \right) + P\left( \bar{A} \right) \times P\left( B \right)\]
\[ = \frac{1}{7}\left( 1 - \frac{1}{5} \right) + \left( 1 - \frac{1}{7} \right)\frac{1}{5}\]
\[ = \frac{1}{7} \times \frac{4}{5} + \frac{6}{7} \times \frac{1}{5}\]
\[ = \frac{4}{35} + \frac{6}{35}\]
\[ = \frac{10}{35} = \frac{2}{7}\]
\[\left( iii \right) P\left( \text{ none of them get selected } \right) = P\left( \bar{B} \right) \times P\left( \bar{A} \right)\]
\[ = \left( 1 - \frac{1}{5} \right) \times \left( 1 - \frac{1}{7} \right)\]
\[ = \frac{4}{5} \times \frac{6}{7}\]
\[ = \frac{24}{35}\]
APPEARS IN
संबंधित प्रश्न
A and B throw a die alternatively till one of them gets a number greater than four and wins the game. If A starts the game, what is the probability of B winning?
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 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
In a shop X, 30 tins of pure ghee and 40 tins of adulterated ghee which look alike, are kept for sale while in shop Y, similar 50 tins of pure ghee and 60 tins of adulterated ghee are there. One tin of ghee is purchased from one of the randomly selected shops and is found to be adulterated. Find the probability that it is purchased from shop Y. What measures should be taken to stop adulteration?
A coin is tossed three times, if head occurs on first two tosses, find the probability of getting head on third toss.
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).
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 (A ∩ B) = 0.32 and P (B) = 0.5, find P (A/B).
If P (A) = 0.4, P (B) = 0.8, P (B/A) = 0.6. Find P (A/B) and P (A ∪ B).
If A and B are two events such that \[ P\left( A \right) = \frac{1}{3}, P\left( B \right) = \frac{1}{4} \text{ and } P\left( A \cup B \right) = \frac{5}{12}, \text{ then find } P\left( A|B \right) \text{ and } P\left( B|A \right) . \]
Two coins are tossed once. Find P (A/B) in each of the following:
A = No tail appears, B = No head appears.
A pair of dice is thrown. Find the probability of getting the sum 8 or more, if 4 appears on the first die.
Two numbers are selected at random from integers 1 through 9. If the sum is even, find the probability that both the numbers are odd.
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 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 a king or queen, B = the card drawn is a queen or jack.
Given two independent events A and B such that P (A) = 0.3 and P (B) `= 0.6. Find P ( overlineA ∩ B) .`
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.
A speaks truth in 75% and B in 80% of the cases. In what percentage of cases are they likely to contradict each other in narrating the same incident?
Tickets are numbered from 1 to 10. Two tickets are drawn one after the other at random. Find the probability that the number on one of the tickets is a multiple of 5 and on the other a multiple of 4.
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 card is drawn from a well-shuffled deck of 52 cards. The outcome is noted, the card is replaced and the deck reshuffled. Another card is then drawn from the deck.
(i) What is the probability that both the cards are of the same suit?
(ii) What is the probability that the first card is an ace and the second card is a red queen?
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?
The bag A contains 8 white and 7 black balls while the bag B contains 5 white and 4 black balls. One ball is randomly picked up from the bag A and mixed up with the balls in bag B. Then a ball is randomly drawn out from it. Find the probability that ball drawn is white.
6 boys and 6 girls sit in a row at random. Find the probability that all the girls sit together.
Write the probability that a number selected at random from the set of first 100 natural numbers is a cube.
If A, B, C are mutually exclusive and exhaustive events associated to a random experiment, then write the value of P (A) + P (B) + P (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
The probability that a leap year will have 53 Fridays or 53 Saturdays 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 coin is tossed three times. If events A and B are defined as A = Two heads come, B = Last should be head. Then, A and B are ______.
A bag contains 5 brown and 4 white socks. A man pulls out two socks. The probability that these are of the same colour is
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
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:
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:
\[\text{ If A and B are two events such that } P\left( A|B \right) = p, P\left( A \right) = p, P\left( B \right) = \frac{1}{3} \text{ and } P\left( A \cup B \right) = \frac{5}{9}, \text{ then} p = \]
Mark the correct alternative in the following question:
\[\text{ Let A and B be two events . If } P\left( A \right) = 0 . 2, P\left( B \right) = 0 . 4, P\left( A \cup B \right) = 0 . 6, \text{ then } P\left( A|B \right) \text{ is equal to} \]
From a set of 100 cards numbered 1 to 100, one card is drawn at random. The probability that the number obtained on the card is divisible by 6 or 8 but not by 24 is
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.
A and B throw a die alternately till one of them gets a '6' and wins the game. Find their respective probabilities of winning, if A starts the game first.
