Advertisements
Advertisements
प्रश्न
A die is tossed twice. Find the probability of getting a number greater than 3 on each toss.
उत्तर
\[S = { \left( 1 1 \right), \left( 1 2 \right), \left( 1 3 \right), \left( 1 4 \right), \left( 1 5 \right), \left( 1 6 \right),} \] \[ \left( 2 1 \right), \left( 2 2 \right), \left( 2 3 \right), \left( 2 4 \right), \left( 2 5 \right), \left( 2 6 \right), \]
\[ \left( 3 1 \right), \left( 3 2 \right), \left( 3 3 \right), \left( 3 4 \right), \left( 3 5 \right), \left( 3 6 \right), \]
\[ \left( 4 1 \right), \left( 4 2 \right), \left( 4 3 \right), \left( 4 4 \right), \left( 4 5 \right), \left( 4 6 \right), \]
\[ \left( 5 1 \right), \left( 5 2 \right), \left( 5 3 \right), \left( 5 4 \right), \left( 5 5 \right), \left( 5 6 \right), \]
\[ \left( 6 1 \right), \left( 6 2 \right), \left( 6 3 \right), \left( 6 4 \right), \left( 6 5 \right), \left( 6 6 \right) \]
\[n\left( S \right) = 36\]
\[E = \text{ Getting a number greater than 3 on each toss } \]
\[ = \left\{ \left( 4 4 \right), \left( 4 5 \right), \left( 4 6 \right), \left( 5 4 \right), \left( 5 5 \right), \left( 5 6 \right), \left( 6 4 \right), \left( 6 5 \right), \left( 6 6 \right) \right\}\]
\[n\left( E \right) = 9\]
\[P\left( E \right) = \frac{9}{36}\]
\[ = \frac{1}{4}\]
APPEARS IN
संबंधित प्रश्न
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.
A bag contains 25 tickets, numbered from 1 to 25. A ticket is drawn and then another ticket is drawn without replacement. Find the probability that both tickets will show even numbers.
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 = No tail appears, B = No head appears.
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.
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?
B = the card drawn is a spade, B = the card drawn in an ace.
If A and B be two events such that P (A) = 1/4, P (B) = 1/3 and P (A ∪ B) = 1/2, show that A and B are independent events.
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.
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 probability that A hits a target is 1/3 and the probability that B hits it, is 2/5, What is the probability that the target will be hit, if each one of A and B shoots at the target?
Two dice are thrown together and the total score is noted. The event E, F and G are "a total of 4", "a total of 9 or more", and "a total divisible by 5", respectively. Calculate P(E), P(F) and P(G) and decide which pairs of events, if any, are independent.
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 - (1 - p_1 )(1 -p_2 ) `
Two balls are drawn at random with replacement from a box containing 10 black and 8 red balls. Find the probability that first ball is black and second is red.
Kamal and Monica appeared for an interview for two vacancies. The probability of Kamal's selection is 1/3 and that of Monika's selection is 1/5. Find the probability that
(i) both of them will be selected
(ii) none of them will be selected
(iii) at least one of them will be selected
(iv) only one of them will be selected.
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?
Arun and Tarun appeared for an interview for two vacancies. The probability of Arun's selection is 1/4 and that to Tarun's rejection is 2/3. Find the probability that at least one of them will be selected.
A and B toss a coin alternately till one of them gets a head and wins the game. If A starts the game, find the probability that B will win the game.
Two cards are drawn from a well shuffled pack of 52 cards, one after another without replacement. Find the probability that one of these is red card and the other a black card?
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 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 none of them will be selected?
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.
The probability of student A passing an examination is 2/9 and of student B passing is 5/9. Assuming the two events : 'A passes', 'B passes' as independent, find the probability of : (i) only A passing the examination (ii) only one of them passing the examination.
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.
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.
If A and B are two independent events such that P (A) = 0.3 and P (A ∪ \[B\]) = 0.8. Find P (B).
An unbiased die with face marked 1, 2, 3, 4, 5, 6 is rolled four times. Out of 4 face values obtained, find the probability that the minimum face value is not less than 2 and the maximum face value is not greater than 5.
Write the probability that a number selected at random from the set of first 100 natural numbers is a cube.
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
A person writes 4 letters and addresses 4 envelopes. If the letters are placed in the envelopes at random, then the probability that all letters are not placed in the right envelopes, 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 ______.
Mark the correct alternative in the following question:
\[\text{ Let A and B are two events such that } P\left( A \right) = \frac{3}{8}, P\left( B \right) = \frac{5}{8} \text{ and } P\left( A \cup B \right) = \frac{3}{4} . \text{ Then } P\left( A|B \right) \times P\left( A \cap B \right) \text{ is equals to } \]
If A and B are two events such that A ≠ Φ, B = Φ, then
Mark the correct alternative in the following question: A bag contains 5 red and 3 blue balls. If 3 balls are drawn at random without replacement, then the probability of getting exactly one red 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:
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
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.
