- A basket contains 8 Blue and 10 Brown balls. There is another basket which contains 6 Blue and 8 Brown balls. One ball is to drawn from either of the two baskets. What is the probability of drawing a Blue ball?
P(choosing 1 basket)=1/2
P(Blue ball from 1st basket)=1/2*8C1/18C1=4/18
P(Blue ball from 2nd basket)=1/2*6C1/14C1=3/14
- One card is drawn at random from a pack of 52 cards. What is the probability that the card drawn is either a black card or a queen?
There are 26 black cards and 4 queen(2queen included in black cards)
- A bag contains 12 Green and 8 White balls. Four balls are drawn out one by one and not replaced. What is the probability that they are in alternate colours?
- From a group of 4 men, 5 women and 3 children, 4 people are to be chosen to form a committee. What is the probability that the committee contains at least 1 each of men, women and children?
No of ways 2M+1W+1C or 1M+2W+1C or 1M+1W+2C
P=(4C2*5C1*3C1 + 4C1*5C2*3C1+ 4C1*5C1*3C2)/12C4
- 8 persons are seated at a round table. What is the probability that 3 particular persons sit together?
3 particular person always sit together, then total person =5+1=6
6 persons will sit in (6-1)!=5! At round table.
No of ways in which 3 persons always sit together=5!*3!
No of ways of sitting 8 persons at round table=(8-1)!=7!.
Then P= (5!*3!)/7! =1/7.
- In a lottery, there are 12prizes and 25 blanks. A lottery is drawn at random. What is the probability of getting a prize?
Question 7-8: In a bag , there are 5 Blue, 7 white and some Red balls. A ball is randomly selected and the probability that the ball is red is 2/5.
- ind the total number of balls?
Then P(Blue and White)=1-2/5=3/5
1 ……… ?==> 20balls.
- If two balls are selected randomly, then what is the probability the selected balls are of same colour?
P(balls are of same colour)=(5C2+7C2+8C2)/20C2
- A and B wrote an exam. The probability of A’s pass is 2/7 and the probability of B’s pass is 2/5. What is the probability that only one of them is passed out?
A’= A’s fail and B’= B’s fail.
Therefore, p(A) = 2/7 and p(B) = 2/5,
P(A’) = 1 – P(A) = 1- 2/7 = 5/7 and P(B’) = 1- P(B) = 1- 1/5 = 4/5
Required probability= (2/7 * 4/5) + (2/5 * 5/7)
= (8/35 + 10/35) = 18/35.
- In a school, 35% of the students play chess,45% play carom and 10% play both. If a student is selected at random, then the probability that he plays chess or carom is
P(A or B)=P(A) + P(B)-P(A and B)