Advertisements
Advertisements
Question
A bag contains 7 red and 4 black balls, 3 balls are drawn at random. Find the probability that all are red
Solution
Let S be the sample space
A be the event of taking 3 red balls and B be the event of taking one red and
2 black balls.
A bag contains 7 red balls and 3 black balls.
3 balls are drawn at random.
∴ The number of outcomes n(S) = 11C3
= `(11 xx 10 xx 9)/(1 xx 2 xx 3)`
= 11 × 5 × 3
= 165
n(A) = 7C3
= `(7 xx 6 xx 5)/(1 xx 2 xx 3)`
= 35
n(B) = 7C1 × 4C2
= `7 xx (4 xx 3)/(1 xx 2)`
= 7 × 6
= 42
P(getting 3 red balls) = P(A)
= `("n"("A"))/("n"("S"))`
= `35/165`
= `7/33`
APPEARS IN
RELATED QUESTIONS
Suppose one person is selected at random from a group of 100 persons are given in the following
| Title | Psychologist | Socialist | Democrat | Total |
| Men | 15 | 25 | 10 | 50 |
| Women | 20 | 15 | 15 | 50 |
| Total | 35 | 40 | 25 | 100 |
What is the probability that the man selected is a Psychologist?
Three boxes B1, B2, B3 contain lamp bulbs some of which are defective. The defective proportions in box B1, box B2 and box B3 are respectively `1/2`, `1/8` and `3/4`. A box is selected at random and a bulb drawn from it. If the selected bulb is found to be defective, what is the probability that box B1 was selected?
Three horses A, B, C are in the race. A is twice as likely to win as B and B is twice as likely to win as C. What are their respective probabilities of winning?
A die is thrown. Find the probability of getting
- a prime number
- a number greater than or equal to 3
There are 1000 students in a school out of which 450 are girls. It is known that out of 450, 20% of the girls studying in class XI. A student is randomly selected from 1000 students. What is the probability that the selected student is from class XI given that the selected student is a girl?
A company has three machines A, B, C which produces 20%, 30% and 50% of the product respectively. Their respective defective percentages are 7, 3 and 5. From these products, one is chosen and inspected. If it is defective what is the probability that it has been made by machine C?
The probability of obtaining an even prime number on each die, when a pair of dice is rolled is
A committee of two persons is formed from 3 men and 2 women. What is the probability that the committee will have
- No woman
- One man
- No man
Data on readership of a magazine indicates that the proportion of male readers over 30 years old is 0.30 and the proportion of male readers under 30 is 0.20. If the proportion of readers under 30 is 0.80. What is the probability that a randomly selected male subscriber is under 30?
An experiment has the four possible mutually exclusive and exhaustive outcomes A, B, C, and D. Check whether the following assignments of probability are permissible.
P(A) = `2/5`, P(B) = `3/5`, P(C) = `- 1/5`, P(D) = `1/5`
Eight coins are tossed once, find the probability of getting exactly two tails
Eight coins are tossed once, find the probability of getting atleast two tails
Eight coins are tossed once, find the probability of getting atmost two tails
A bag contains 7 red and 4 black balls, 3 balls are drawn at random. Find the probability that one red and 2 black
Suppose P(B) = `2/5`. Express the odds event B occurs
Choose the correct alternative:
Four persons are selected at random from a group of 3 men, 2 women and 4 children. The probability that exactly two of them are children is
Choose the correct alternative:
A bag contains 6 green, 2 white, and 7 black balls. If two balls are drawn simultaneously, then the probability that both are different colours is
Choose the correct alternative:
An urn contains 5 red and 5 black balls. A ball is drawn at random, its colour is noted and is returned to the urn. Moreover, 2 additional balls of the colour drawn are put in the urn and then a ball is drawn at random. The probability that the second ball drawn is red will be
