Advertisements
Advertisements
Question
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
Options
0.024
0.452
0.336
0.188
Solution
\[\text{ Let } : \]
\[\text{ A be the event of hitting the target by the person A } , \]
\[\text{ B be the event of hitting the target by the person B and } \]
\[\text{ C be the event of hitting the target by the person C } \]
\[\text{ We have} , \]
\[P\left( A \right) = 0 . 4, P\left( B \right) = 0 . 3 \text{ and } P\left( C \right) = 0 . 2\]
\[\text{ Also} , \]
\[P\left(\overline{A} \right) = 1 - P\left( A \right) = 1 - 0 . 4 = 0 . 6, \]
\[P\left( \overline{B} \right) = 1 - 0 . 3 = 0 . 7 \text{ and } \]
\[P\left( \overline{C} \right) = 1 - 0 . 2 = 0 . 8\]
\[\text{ Now } , \]
\[P\left( \text{ Two hits } \right) = P\left( AB\overline{C} \right) + P\left( A\overline{B}C \right) + P\left( \overline{A}BC \right)\]
\[ = P\left( A \right) \times P\left( B \right) \times P\left(\overline{ C } \right) + P\left( A \right) \times P\left( \overline{B} \right) \times P\left( C \right) + P\left(\overline{ A} \right) \times P\left( B \right) \times P\left( C \right)\]
\[ = 0 . 4 \times 0 . 3 \times 0 . 8 + 0 . 4 \times 0 . 7 \times 0 . 2 + 0 . 6 \times 0 . 3 \times 0 . 2\]
\[ = 0 . 096 + 0 . 056 + 0 . 036\]
\[ = 0 . 188\]
APPEARS IN
RELATED QUESTIONS
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.
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'.
A coin is tossed three times, if head occurs on first two tosses, find the probability of getting head on third toss.
Find the chance of drawing 2 white balls in succession from a bag containing 5 red and 7 white balls, the ball first drawn not being replaced.
A bag contains 5 white, 7 red and 3 black balls. If three balls are drawn one by one without replacement, find the probability that none is red.
Two coins are tossed once. Find P (A/B) in each of the following:
A = No tail appears, B = No head appears.
Find the probability that the sum of the numbers showing on two dice is 8, given that at least one die does not show five.
In a school there are 1000 students, out of which 430 are girls. It is known that out of 430, 10% of the girls study in class XII. What is the probability that a student chosen randomly studies in class XII given that the chosen student is a girl?
Ten cards numbered 1 through 10 are placed in a box, mixed up thoroughly and then one card is drawn randomly. If it is known that the number on the drawn card is more than 3, what is the probability that it is an even number?
Prove that in throwing a pair of dice, the occurrence of the number 4 on the first die is independent of the occurrence of 5 on the second die.
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.
A coin is tossed three times. Let the events A, B and C be defined as follows:
A = first toss is head, B = second toss is head, and C = exactly two heads are tossed in a row.
Check the independence of A and B.
Given two independent events A and B such that P (A) = 0.3 and P (B) = 0.6. Find \[P \overline A \cup \overline B \] .
Given two independent events A and B such that P (A) = 0.3 and P (B) = 0.6. Find P (A/B) .
Given two independent events A and B such that P (A) = 0.3 and P (B) = 0.6. Find P (B/A) .
If A and B are two independent events such that P (A ∪ B) = 0.60 and P (A) = 0.2, find P(B).
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.
A bag contains 3 red and 5 black balls and a second bag contains 6 red and 4 black balls. A ball is drawn from each bag. Find the probability that one is red and the other is black.
Two balls are drawn at random with replacement from a box containing 10 black and 8 red balls. Find the probability that both the balls are red.
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.
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?
In a family, the husband tells a lie in 30% cases and the wife in 35% cases. Find the probability that both contradict each other on the same fact.
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 only one of them will be selected ?
Three cards are drawn with replacement from a well shuffled pack of 52 cards. Find the probability that the cards are a king, a queen and a jack.
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.
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.
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?
An unbiased coin is tossed. If the result is a head, a pair of unbiased dice is rolled and the sum of the numbers obtained is noted. If the result is a tail, a card from a well shuffled pack of eleven cards numbered 2, 3, 4, ..., 12 is picked and the number on the card is noted. What is the probability that the noted number is either 7 or 8?
A four digit number is formed using the digits 1, 2, 3, 5 with no repetitions. Write the probability that the number is divisible by 5.
If A and B are independent events such that P(A) = p, P(B) = 2p and P(Exactly one of Aand B occurs) = \[\frac{5}{9}\], then find the value of p.
If A and B are two events, then P (`overline A` ∩ B) =
Mark the correct alternative in the following question:
\[\text{ If} P\left( A \right) = 0 . 4, P\left( B \right) = 0 . 8 \text{ and } P\left( B|A \right) = 0 . 6, \text{ then } P\left( A \cup B \right) = \]
Mark the correct alternative in the following question:
Two dice are thrown. If it is known that the sum of the numbers on the dice was less than 6, then the probability of getting a sum 3, is
An insurance company insured 3000 cyclists, 6000 scooter drivers, and 9000 car drivers. The probability of an accident involving a cyclist, a scooter driver, and a car driver are 0⋅3, 0⋅05 and 0⋅02 respectively. One of the insured persons meets with an accident. What is the probability that he is a cyclist?
