Advertisements
Advertisements
प्रश्न
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
उत्तर
Total of 7 on the dice can be obtained in the following ways:
(1, 6), (6, 1), (2, 5), (5, 2), (3, 4), (4, 3)
Probability of getting a total of 7 = `6/36=1/6`
Probability of not getting a total of 7 = `1-1/6=5/6`
Total of 10 on the dice can be obtained in the following ways:
(4, 6), (6, 4), (5, 5)
Probability of getting a total of 10 = `3/36=1/12`
Probability of not getting a total of 10 = `1-1/12=11/12`
Let E and F be the two events, defined as follows:
E = Getting a total of 7 in a single throw of a dice
F = Getting a total of 10 in a single throw of a dice
`P(E)=1/6, P(barE)=5/6P(F)=1/12, P(barF)=11/12`
A wins if he gets a total of 7 in 1st, 3rd or 5th ... throws
Probability of A getting a total of 7 in the 1st throw = `1/6`
A will get the 3rd throw if he fails in the 1st throw and B fails in the 2nd throw.
Probability of A getting a total of 7 in the 3rd throw = `P(barE)P(barF)P(barE)=5/6xx11/12xx1/6`
Similarly, probability of getting a total of 7 in the 5th throw = `P(barE)P(barF)P(barE)P(barF)P(E)=5/6xx11/12xx5/6xx11/12xx1/6 " an so on"`
Probability of winning of A = `1/6+(5/6xx11/12xx1/6)+(5/6xx11/12xx5/6xx11/12xx1/6)+...=(1/6)/(1-5/6xx11/12)=12/17`
∴ Probability of winning of B = 1 − Probability of winning of A =`1-12/17=5/17`
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.
A card is drawn from a well-shuffled deck of 52 cards and then a second card is drawn. Find the probability that the first card is a heart and the second card is a diamond if the first card is not replaced.
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).
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 dice is thrown twice and the sum of the numbers appearing is observed to be 6. What is the conditional probability that the number 4 has appeared at least once?
A pair of dice is thrown. Find the probability of getting the sum 8 or more, if 4 appears on the first die.
The probability that a student selected at random from a class will pass in Mathematics is `4/5`, and the probability that he/she passes in Mathematics and Computer Science is `1/2`. What is the probability that he/she will pass in Computer Science if it is known that he/she has passed in Mathematics?
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 black, B = the card drawn is a king.
An anti-aircraft gun can take a maximum of 4 shots at an enemy plane moving away from it. The probabilities of hitting the plane at the first, second, third and fourth shot are 0.4, 0.3, 0.2 and 0.1 respectively. What is the probability that the gun hits the plane?
Two balls are drawn at random with replacement from a box containing 10 black and 8 red balls. Find the probability that one of them is black and other is red.
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?
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.
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.
In a hockey match, both teams A and B scored same number of goals upto the end of the game, so to decide the winner, the refree asked both the captains to throw a die alternately and decide that the team, whose captain gets a first six, will be declared the winner. If the captain of team A was asked to start, find their respective probabilities of winning the match and state whether the decision of the refree was fair or not.
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.
6 boys and 6 girls sit in a row at random. Find the probability that all the girls sit together.
If A and B are two independent events such that P (A) = 0.3 and P (A ∪ \[B\]) = 0.8. Find P (B).
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).
Three faces of an ordinary dice are yellow, two faces are red and one face is blue. The dice is rolled 3 times. The probability that yellow red and blue face appear in the first second and third throws respectively, is
Three integers are chosen at random from the first 20 integers. The probability that their product is even is
Choose the correct alternative in the following question:
Associated to a random experiment two events A and B are such that
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, B and C throw a pair of dice in that order alternatively till one of them gets a total of 9 and wins the game. Find their respective probabilities of winning, if A starts first.
