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#### Introduction To Probability Theory Two Marks Questions Paper

11th Standard

Reg.No. :
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Maths

Time : 00:45:00 Hrs
Total Marks : 30
15 x 2 = 30
1. If an experiment has exactly the three possible mutually exclusive outcomes A, B, and C, check in each case whether the assignment of probability is permissible
$P(A)=\frac { 2 }{ 5 } ,\quad P(B)=\frac { 1 }{ 5 } ,\quad P(C)=\frac { 3 }{ 5 }$

2. If an experiment has exactly the three possible mutually exclusive outcomes A, B, and C, check in each case whether the assignment of probability is permissible
P(A)=0.421, P(B)=0.527  P(C)=0.042

3. There are two identical urns containing respectively 6 black and 4 red balls, 2 black and 2 red balls. An urn is chosen at random and a ball is drawn from it.
(i) find the probability that the ball is black
(ii) if the ball is black, what is the probability that it is from the first urn?

4. If two coins are tossed simultaneously, then find the probability of getting
(i) one head and one tail (ii) at most two tails

5. Five mangoes and 4 apples are in a box. If two fruits are chosen at random, find the probability that (i) one is a mango and the other is an apple (ii) both are of the same variety

6. A bag contains 7 red and 4 black balls, 3 balls are drawn at random. Find the probability that (i) all are red (ii) one red and 2 black

7. A single card is drawn from a pack of 52 cards. What is the probability that
The card is an ace or a king?

8. A cricket club has 16 members, of whom only 5 can bowl. What is the probability that in a team of 11 members at least 3 bowlers are selected

9. Nine coins are tossed once, find the probability to get at least two heads

10. Given that P(A) =0.52, P(B)=0.43, and P(A∩B)=0.24, find
P$\left( A\cap \overline { B } \right)$

11. Given that P(A) =0.52, P(B)=0.43, and P(A∩B)=0.24, find
$P(\overline { A } \cup \overline { B } )$

12. If P($\bar { A }$) = 0.6 P(B) = 0.7 and $P\left( \frac { B }{ A } \right) =0.4$ , then find $P\left( \frac { A }{ B } \right)$and $P(A\cup B)$

13. The probability that student selected at random from a class will pass in Mathematics is $\frac { 2 }{ 3 }$ and the probability that he passes in Mathematics and English is $\frac { 1 }{ 3 }$. What is the probability that he will pass in English if it is known that he has passed in Mathematics?

14. A die is tossed thrice. find the probability of getting an odd number atleast once?

15. Given that the events A and B are such that P(A) = $\frac { 1 }{ 2 }$, P(AUB) = $\frac { 3 }{ 5 }$ and P(B) = p. find P if they are mutually exclusive events.