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Published on: 18/10/2019
Probability
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1.
20 cards are numbered from 1 to 20.In those of them, one card is drawn at random.What is the probability that the number on the card drawn is an odd number?
2.
A die is thrown, find the probability of getting an even number.
3.
A card is selected from a pack of 52 cards.Find the probability that the card is an ace of club.
4.
If the odds against winning a race of three horses are respectively 3:1, 4:1 and 5:1, then what is the probability that on of these horses will win?
5.
Find the probability that, when a hand of 5 cards is drawn from a well-shuffled deck of 52 cards, it contains 3 queens.
6.
Two dice are thrown find odds in favour of getting the sum 5.
7.
A coin is tossed and a die is thrown. Find the probability that the outcomes will be a tail or a number greater than 3.
8.
In a single throw of three dice, find the probability of getting a total of 17 or 18
9.
One card is drawn from a well-shuffled deck of 52 cards.Calculate the probability that the card will be
not an ace
10.
One card is drawn from a well-shuffled deck of 52 cards.Calculate the probability that the card will be
a black card
11.
In a drawing competition, the odds in favour of competitors A, B, C and D are 1:2,1:3,1:4 and 1:5, respectively. Find the probability that one of them wins the competition.
12.
A bag contains 6 discs of which 4 red,3 are blue and 2 are yellow.The discs are similar in shape and size.A disc is drawn at random from the bag.Calculate the probability that it will be
either red or blue
13.
If \(\frac { 5 }{ 14 } \)is the probability of occurrence of an event, find the odd against its occurrence.
14.
In a large metropolitan area, the probabilities are 0.87,0.36,0.30 that a family (randomly chosen for a sample survey) owns a colour television set, a black and white television set, or both kinds of sets. What is the probability that a family owns either anyone or both kinds of sets?
15.
Find the probability of getting atmost two heads or atleast two tails in a toss of three coins.
1.
Favourable outcomes are 1,3,5,7,9,11,13,15,17 and 19
\(\frac { 1 }{ 2 } \)
2.
\(\frac { 1 }{ 2 } \)
3.
\(\frac { 1 }{ 52 } \)
4.
\(\frac { 37 }{ 60 } \)
5.
\(\frac { 47 }{ 10829 } \)
6.
Let S be the sample space associated with the given random experiment. Then, n(S)=36
Let E be the event of getting the sum 5. Then,
E={(1,4), (4,1),(2,3),(3,2)}
\(\Rightarrow n(E)=4\)
\(\therefore p(E)=\frac { n(E) }{ n(S) } =\frac { 4 }{ 36 } =\frac { 1 }{ 9 } \Rightarrow P(\overline { E) } =1-\frac { 1 }{ 9 } =\frac { 8 }{ 9 } \)
Hence, odds in favour of getting the sum 5 \(= \frac { p\left( E \right) }{ P\overline { \left( E \right) } } \)
Ans. 1:8
7.
\(\frac { 3 }{ 4 } \)
8.
\(\frac { 1 }{ 54 } \)
9.
\(\frac { 12 }{ 13 } \)
10.
\(\frac { 1 }{ 2 } \)
11.
Let E1, E2, E3 and E4 be the events that the competitors A, B, C and D respectively win the competition.
Then, P(E1)=\(\frac { 1 }{ 3 } \);P(E2)=\(\frac { 1 }{ 4 } \);P(E3)=\(\frac { 1 }{ 5 } \) and P(E4)=\(\frac { 1 }{ 6 } \)
Now, required probability
=P(E1\(\cup \)E2\(\cup \)E3\(\cup \)E4) = P(E1) + P(E2) + P(E3) + P(E4)
Ans. \(\frac { 114 }{ 120 } \)
12.
\(\frac { 7 }{ 9 } \)
13.
\(Let \ P(E)=\frac { 5 }{ 14 } .Then\ P(\overline { E } )=1-P(E)=1-\frac { 5 }{ 14 } =\frac { 9 }{ 14 } \)
Odds against the occurrence of event \(E=\frac { P(\overline { E } ) }{ P(E) } \)
Ans. \(\frac { 9 }{ 5 } \)
14.
Let A be the event that the family owns a colour television set and B be the event that the family owns a black and white television.Then, we have P(A) = 0.87, P(B) = 0.36, P(A\(\cap \)B) = 0.30
Ans. 0.93
15.
\(\frac { 7 }{ 8 } \)
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