A bag contains 5 red bottles, 6 yellowbottles and 8 greenbottles . 3bottles are drawn randomly. What is the probability that thebottles drawn contain exactly two yellow bottles ?

Total number of bottles = 5 + 6 + 8 = 19 Let S be the sample space. Then, n(S) = number of ways of drawing 3 bottles out of 19 =^{19}C_{3} = `(19 xx 18 xx 17)/ (3 xx 2 xx 1)` = 969 Let E = event of drawing e xactly two yellow bottles n(E) =^{6}C_{2}`xx` ^{13}C_{1}=`(6 xx 5)/(2 xx 1)` `xx` 13 = 195

`:.` P(E) = `(n(E))/(n(S))` = `195/969` = `65/323`

- In a lottery, there are 12 prizes and 16 blanks. A lottery is drawn at random. What is the probability of getting a prize?
- A box contains 5 blue jellies, some red jelly and rest yellow jelly. The probability of picking a red ball at random is 3/10, while the probability of picking a yellow ball at random is 1/5. Find the total number of jellies in the box.
- In a factory which manufactures calculators, machines A, B and C manufacture respectively 25%, 35% and 40% of the calculators. Of their outputs, 5, 4 and 2 percent are respectively defective calculators. A calculator is drawn at random from the product and is found to be defective. What is the probability that it is manufactured by the machine B?
- In a lottery, there are 6 prizes and 30 blanks. A lottery is drawn at random. What is the probability of getting a prize?
- If three socks are chosen at random, what is the probability that all are blue socks?
- If the letters of the word HORIZON be arranged at random, what is the probability that vowels are not together?
- Tokens numbered 1 to 350 are in a bag. What is the probability that the Token drawn has a number which is a multiple of 6 or 7?
- A bag contains 8 black and 10 white balls. One ball is drawn at random. What is the probability that the ball drawn is white?
- A black and a red dice are rolled. Find the conditional probability of obtaining a sum greater than 9, given that the black die resulted in a 5.
- Two hats are picked at random, what is the probability that all hats are of green colour?

More Probability Questions

×

×