Advertisements
Advertisements
प्रश्न
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.
उत्तर
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
संबंधित प्रश्न
In a lottery of 50 tickets numbered 1 to 50, one ticket is drawn. Find the probability that the
drawn ticket bears a prime number.
From a pack of 52 playing cards Jacks, queens, kings and aces of red colour are removed. From the remaining, a card is drawn at random. Find the probability that the card drawn is A red card
It is given that m a group of 3 students, the probability of 2 students not having the same birthday is 0.992. What is the probability that the 2 students have the same birthday?
From a deck of 52 cards, all the face cards are removed and then the remaining cards are shuffled. Now one card is drawn from the remaining deck. Find the probability that the card drawn is a black card.
Find the probability that in a leap year there will be 53 Tuesdays ?
A dice is thrown once. What is the probability that the number is even?
Two dice are thrown at the same time. Find the probability of getting different numbers on both dice.
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
In a game, the entry fee is Rs 5. The game consists of a tossing a coin 3 times. If one or two heads show, Sweta gets her entry fee back. If she throws 3 heads, she receives double the entry fees. Otherwise she will lose. For tossing a coin three times, find the probability that she gets double entry fee.
At a fete, cards bearing numbers 1 to 1000, one number on one card, are put in a box. Each player selects one card at random and that card is not replaced. If the selected card has a perfect square greater than 500, the player wins a prize. What is the probability that the second player wins a prize, if the first has won?
