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Published on: 18/09/2019
Probability
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1.
Two die are rolled together what is the probability that the sum of numbers on the two faces is neither divisible by 4 nor by 5?
2.
A card is drawn from a pack of 52 cards. Find the probability that
(i) one is an ace and other is black queen (ii)one is heart and the other is a spade
3.
If A and B are two mutually exclusive events in a sample space such that P(A) = 0.3 and P(B)= 0.6 then find \(P(\overline { B) } \)
4.
If A and B are two mutually exclusive events in a sample space such that P(A) = 0.3 and P(B)= 0.6 then find P(A).
5.
Two die are thrown simultaneously. Find the probability of getting four as the product.
6.
If \(\frac { 3 }{ 7 } \) is the probability of an event A, what is the probability of the event 'not A'.
7.
Consider the experiment in which a coin is tossed repeatedly until a head comes up. Describe the sample space of the experiment.
8.
A die is tossed. Let E denotes the event of getting a number multiple of 2 and F denotes the event of getting a number less than 7. Simplify the following event. F-E
9.
Find the probability that in a random arrangement of the letters of the word 'SOCIAL' vowels come together.
10.
A die is rolled. If the outcome is an odd number, then what is the probability that it is a prime number?
11.
Two dice are rolled. Let E1, E2, and E3 be the events of getting a sum of 4, 5 and respectively.
Which events are elementary events?
12.
Consider the following experiment of rolling a die.Let A be the event 'getting a prime number' and B be the event'getting an odd number'.Write the sets representing events
A or B
13.
What is the probability of drawing a 'king' from a well-shuffled deck of 52 cards?
14.
If A and B are two events associated with a random experiment such that P(A)=0.3.P(B)=0.2 and \(P(A\cap B)=0.1\) ,then find the value of \(P(A\cap B)\)
15.
Five marbles are drawn from a bag which contains 7 blue marbles and 4 black marbles. What is the probability that 3 will be blue and 2 black?
1.
\(\frac { 5 }{ 9 } \)
2.
(i) \(\frac { 4 }{ 663 } \)
(ii) \(\frac { 13 }{ 102 } \)
3.
0.4
4.
0.7
5.
Let S be the sample space. Then n(S) = 36.
Let A be the event getting four as product.
i.e., {(I, 4), (2, 2), (4, I)}
\(\therefore \) n(A) = 3
\(P(A)=\frac { n(A) }{ n(S) } =\frac { 3 }{ 6 } =\frac { 1 }{ 12 } \)
6.
Here P(A)=\(\frac { 3 }{ 7 } \)
We know that \(P\left( \overline { A } \right) \)
=\(1-\frac { 3 }{ 7 } =\frac { 4 }{ 7 } \)
7.
{H, TH, TTH, TTTH, ...}
8.
E={2,4,6} and F={1,2,3,4,5,6}
{1,3,5}
9.
Total outcomes = 6!
Favourable outcomes = 4! x 3!
\(\frac { 1 }{ 5 } \)
10.
On rolling a die, we get outcomes as odd number.So,sample space, S = (1,3,5} \(\Rightarrow \) n(S) = 3
Let E be the event of getting a prime number then,
E={3,5} \(\Rightarrow \) n(E) = 2
Required probability = \(\frac { n(E) }{ n(S) } =\frac { 2 }{ 3 } \)
11.
E1={(1,3),(2,2), (3,1)}
E2={(1,4),(2,3),(3,2),(4,1)}
E3={(1,5),(2,4),(3,3),(5,1),(4,2)}
No event
12.
{1,2,3,5}
13.
probability =\(\frac { ^{ 4 }{ C }_{ 1 } }{ ^{ 52 }{ C }_{ 1 } } \)
14.
0.2
15.
\(\frac { 5 }{ 11 } \)
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