Advertisements
Advertisements
Question
A and B throw a pair of dice alternately. A wins the game if he gets a total of 6 and B wins if she gets a total of 7. It A starts the game, find the probability of winning the game by A in third throw of the pair of dice.
Solution
Let A1 be the event of getting a total of 6
= {(2, 4), (4, 2), (1, 5), (5, 1), (3, 3)}
And B1 be the event of getting a total of 7
= {(2, 5), (5, 2), (1, 6), (6, 1), (3, 4), (4, 3)}
Let P(A1) is the probability, if A wins in a throw = `5/36`
And P(B1) is the probability, if B wins in a throw = `1/6`
∴ The required probability of winning A in his third throw
= `"P"(bar"A"_1) * "P"(bar"B"_1) * "P"("A"_1)`
= `31/36 * 5/6 * 5/36`
= `775/7776`.
APPEARS IN
RELATED QUESTIONS
A pair of dice is thrown 6 times. If getting a total of 9 is considered a success, what is the probability of at least 5 successes?
A fair coin is tossed 8 times, find the probability of exactly 5 heads .
Find the probability of 4 turning up at least once in two tosses of a fair die.
A pair of dice is thrown. What is the probability of getting an even number on the first die or a total of 8?
An urn contains 25 balls of which 10 balls are red and the remaining green. A ball is drawn at random from the urn, the colour is noted and the ball is replaced. If 6 balls are drawn in this way, find the probability that:
(i) All the balls are red.
(ii) Not more than 2 balls are green.
(iii) The number of red balls and green balls is equal.
In a bolt factory, three machines A, B, and C manufacture 25%, 35% and 40% of the total production respectively. Of their respective outputs, 5%, 4% and 2% are defective. A bolt is drawn at random from the total production and it is found to be defective. Find the probability that it was manufactured by machine C.
A committee of 4 persons has to be chosen from 8 boys and 6 girls, consisting of at least one girl. Find the probability that the committee consists of more girls than boys.
State the sample space and n(S) for the following random experiment.
A coin is tossed twice. If a second throw results in head, a die thrown, otherwise a coin is tossed.
A coin and a die are tossed. State sample space of following event.
A: Getting a head and an even number.
Find total number of distinct possible outcomes n(S) of the following random experiment.
From a box containing 25 lottery tickets any 3 tickets are drawn at random.
Find total number of distinct possible outcomes n(S) of the following random experiment.
6 students are arranged in a row for a photograph.
Two dice are thrown. Write favourable outcomes for the following event.
Q: Sum of the numbers on two dice is 7.
Two dice are thrown. Write favourable outcomes for the following event.
R: Sum of the numbers on two dice is a prime number.
Also, check whether Events Q and R are mutually exclusive and exhaustive.
A card is drawn at random from an ordinary pack of 52 playing cards. State the number of elements in the sample space if consideration of suits is taken into account.
Box-I contains 8 red (R11, R12, R13) and 2 blue (B11, B12) marbles while Box-II contains 2 red(R21, R22) and 4 blue (B21, B22, B23, B24) marbles. A fair coin is tossed. If the coin turns up heads, a marble is chosen from Box-I; if it turns up tails, a marble is chosen from Box-II. Describe the sample space.
A car manufacturing factory has two plants, X and Y. Plant X manufactures 70% of cars and plant Y manufactures 30%. 80% of the cars at plant X and 90% of the cars at plant Y are rated of standard quality. A car is chosen at random and is found to be of standard quality. What is the probability that it has come from plant X?
Prove that P(A ∪ B) = `"P"("A" ∩ "B") + "P"("A" ∩ bar"B") + "P"(bar"A" ∩ bar"B")`
A die is thrown 5 times. Find the probability that an odd number will come up exactly three times.
The probability of a man hitting a target is 0.25. He shoots 7 times. What is the probability of his hitting at least twice?
Three bags contain a number of red and white balls as follows:
Bag 1:3 red balls, Bag 2:2 red balls and 1 white ball
Bag 3:3 white balls.
The probability that bag i will be chosen and a ball is selected from it is `"i"/6`, i = 1, 2, 3. What is the probability that a red ball will be selected?
Three bags contain a number of red and white balls as follows:
Bag 1:3 red balls, Bag 2:2 red balls and 1 white ball
Bag 3:3 white balls.
The probability that bag i will be chosen and a ball is selected from it is `"i"/6`, i = 1, 2, 3. What is the probability that a white ball is selected?
There are two bags, one of which contains 3 black and 4 white balls while the other contains 4 black and 3 white balls. A die is thrown. If it shows up 1 or 3, a ball is taken from the Ist bag; but it shows up any other number, a ball is chosen from the second bag. Find the probability of choosing a black ball.
A bag contains (2n + 1) coins. It is known that n of these coins have a head on both sides where as the rest of the coins are fair. A coin is picked up at random from the bag and is tossed. If the probability that the toss results in a head is `31/42`, determine the value of n.
A die is thrown and a card is selected at random from a deck of 52 playing cards. The probability of getting an even number on the die and a spade card is ______.
Eight coins are tossed together. The probability of getting exactly 3 heads is ______.
The letters of the word "ATTRACTION' are written randomly. The probability that no two T's appear together is
A bag contains 10 white and 3 black balls. Balls are drawn without replacement till all the black balls are drawn. What is the probability that this procedure will come to an end on the seventh draw?
