Advertisements
Advertisements
Question
Cards marked with numbers 1, 3, 5, ..., 101 are placed in a bag and mixed thoroughly. A card is drawn at random from the bag. Find the probability that the number on the drawn card is a prime number less than 20.
Solution
Given number 1, 3, 5, ..., 101 form an AP with a = 1 and d = 2.
Let Tn = 101. Then,
1 + (n − 1)2 = 101
⇒ 1 + 2n − 2 = 101
⇒ 2n = 102
⇒ n = 51
Thus, total number of outcomes = 51.
Let E2 be the event of getting a prime number less than 20.
Out of these numbers, prime numbers less than 20 are 3, 5, 7, 11, 13, 17 and 19.
Thus, number of favourable outcomes = 7.
∴ P(getting a prime number less than 20) = P(E2) = `("Number of outcomes favourable to" E_2)/"Number of all possible outcomes"`
`= 7/51`
Thus, the probability that the number on the drawn card is a prime number less than 20 is `7/51`.
APPEARS IN
RELATED QUESTIONS
A card is drawn at random from a pack of 52 cards. Find the probability that card drawn is neither an ace nor a king
A card is drawn at random from a pack of 52 cards. Find the probability that card drawn is the seven of clubs
A box contains loo red cards, 200 yellow cards and 50 blue cards. If a card is drawn at random from the box, then find the probability that it will be neither yellow nor a blue card.
For an event E, write a relation representing the range of values of P(E).
Seven cards:- the eight, the nine, the ten, jack, queen, king and ace of diamonds are well shuffled. One card is then picked up at random.
If the king is drawn and put aside, what is the probability that the second card picked up is:
- an ace?
- a king?
A box contains 100 red cards, 200 yellow cards and 50 blue cards. If a card is drawn at random from the box, then find the probability that it will be (i) a blue card (ii) not a yellow card (iii) neither yellow nor a blue card.
A box contains 30 tickets, bearing only one number from 1 to 30 on each. If one ticket is drawn at random, find the probability of an event that the ticket drawn bears an odd number .
A die has 6 faces marked by the given numbers as shown below:
| 1 | 2 | 3 | – 1 | – 2 | – 3 |
The die is thrown once. What is the probability of getting the smallest integer?
All the jacks, queens and kings are removed from a deck of 52 playing cards. The remaining cards are well shuffled and then one card is drawn at random. Giving ace a value 1 similar value for other cards, find the probability that the card has a value 7
Following experiment have equally likely outcomes? Explain.
A trial is made to answer a true-false question. The answer is right or wrong.
