Advertisements
Advertisements
प्रश्न
A bag contains 5 red and 3 blue balls. If 3 balls are drawn at random without replacement the probability of getting exactly one red ball is ______.
विकल्प
`45/196`
`135/392`
`15/56`
`15/29`
उत्तर
A bag contains 5 red and 3 blue balls. If 3 balls are drawn at random without replacement the probability of getting exactly one red ball is `15/56`.
Explanation:
Given that: Bag contains 5 red and 3 blue balls.
Probability of getting exactly one red ball if 3 balls are randomly drawn without replacement
= P(R) . P(B) . P(B) + P(B) . P(R) . P(B) + P(B) . P(B) . P(R)
= `5/8*3/7*2/6 + 3/8*5/7*2/6 + 3/8*2/7*5/6`
= `30/336 + 30/336 + 30/336`
= `90/336`
= `15/56`
APPEARS IN
संबंधित प्रश्न
A coin is tossed 5 times. What is the probability of getting at least 3 heads?
A coin is tossed 5 times. What is the probability that tail appears an odd number of times?
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 at most six heads.
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.
One dialing certain telephone numbers assume that on an average, one telephone number out of five is busy, Ten telephone numbers are randomly selected and dialed. Find the probability that at least three of them will be busy.
A coin and a die are tossed. State sample space of following event.
C: Getting a tail and perfect square.
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 bag contains 5 red marbles and 3 black marbles. Three marbles are drawn one by one without replacement. What is the probability that at least one of the three marbles drawn be black, if the first marble is red?
Prove that P(A) = `"P"("A" ∩ "B") + "P"("A" ∩ bar"B")`
Prove that P(A ∪ B) = `"P"("A" ∩ "B") + "P"("A" ∩ bar"B") + "P"(bar"A" ∩ bar"B")`
Bag I contains 3 black and 2 white balls, Bag II contains 2 black and 4 white balls. A bag and a ball is selected at random. Determine the probability of selecting a black ball.
A box has 5 blue and 4 red balls. One ball is drawn at random and not replaced. Its colour is also not noted. Then another ball is drawn at random. What is the probability of second ball being blue?
Four cards are successively drawn without replacement from a deck of 52 playing cards. What is the probability that all the four cards are kings?
Ten coins are tossed. What is the probability of getting at least 8 heads?
A lot of 100 watches is known to have 10 defective watches. If 8 watches are selected (one by one with replacement) at random, what is the probability that there will be at least one defective watch?
A die is thrown three times. Let X be ‘the number of twos seen’. Find the expectation of X.
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?
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.
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 ______.
Eight coins are tossed together. The probability of getting exactly 3 heads is ______.
Two cards are drawn at random from a pack of 52 cards one-by-one without replacement. What is the probability of getting first card red and second card Jack?
Three horses A, B, Care in a race. A is twice as likely to win as B, and B is twice as likely to win as C. The probability that C wins, P(C) is
In year 2019, the probability of getting 53 Sundays is
Two cards are drawn together from a pack of 52 cards. The probability that one is a spade and one is a heart, is?
Assertion (A): Two coins are tossed simultaneously. The probability of getting two heads, if it is known that at least one head comes up, is `1/3`.
Reason (R): Let E and F be two events with a random experiment, then `P(E/F) = (P(E ∩ F))/(P(E))`.
