[\dfrac{10}{21}] A bag contains 2 red, 3 green and 2 blue balls. Two balls are drawn at random. What is the probabili

For Competitive Exams

A bag contains 2 red, 3 green and 2 blue balls. Two balls are drawn at random. What is the probability that none of the balls drawn is blue?

$ \dfrac{10}{21} $

$ \dfrac{11}{21} $

$ \dfrac{2}{7} $

$ \dfrac{5}{7} $

Explanation:

Total number of balls = (2 + 3 + 2) = 7.

Let S be the sample space.

Then, $ n\left(S\right)$ = Number of ways of drawing 2 balls out of 7

= ⁷C₂ `

=$ \dfrac{(7 \times 6)}{(2 \times 1)} $

= 21.

Let E = Event of drawing 2 balls, none of which is blue.

$\therefore n \left(E\right)$ = Number of ways of drawing 2 balls out of (2 + 3) balls.

= ⁵C₂

=$ \dfrac{(5 \times 4)}{(2 \times 1)} $

= 10.

$\therefore P\left(E\right)$ =$ \dfrac{n(E)}{n(S)} $=$ \dfrac{10}{21} $.

Additional Questions

Two cards are drawn together at random from a pack of 52 cards. What is the probability of both the cards being Queens?	Answer
Two cards are drawn together from a pack of 52 cards. The probability that one is a club and one is a diamond?	Answer
John and Dani go for an interview for two vacancies. The probability for the selection of John is 1/3 and whereas the probability for the selection of Dani is 1/5. What is the probability that only one of them is selected?	Answer
The probability A getting a job is 1/5 and that of B is 1/7 . What is the probability that only one of them gets a job?	Answer
Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is even?	Answer
Two dice are tossed. The probability that the total score is a prime number is:	Answer
From a pack of 52 cards, two cards are drawn together at random. What is the probability of both the cards being kings?	Answer
A card is randomly drawn from a deck of 52 cards. What is the probability getting a five of Spade or Club?	Answer
In a class, there are 15 boys and 10 girls. Three students are selected at random. The probability that 1 girl and 2 boys are selected, is:	Answer
A bag contains 2 red, 3 green and 2 blue balls. Two balls are drawn at random. What is the probability that none of the balls drawn is blue?	Answer

Share with Friends