Advertisements
Advertisements
Question
Cards bearing numbers 1, 3, 5, .... , 35 are kept in a bag. A card is drawn at random from the bag. Find the probability of getting a card bearing a prime number less than 15,
Solution
Given number 1, 3, 5, .... , 35 form an AP with a = 1 and d = 2.
Let Tn = 35. Then,
1 + (n − 1)2 = 35
⇒ 1 + 2n − 2 = 35
⇒ 2n = 36
⇒ n = 18
Thus, total number of outcomes = 18.
Let E1 be the event of getting a prime number less than 15.
Out of these numbers, prime numbers less than 15 are 3, 5, 7, 11 and 13.
Number of favourable outcomes = 5.
∴ P(getting a prime number less than 15) = P(E1) = `("Number of outcomes favourable to" E_1)/"Number of all possible outcomes"`
`=5/18`
Thus, the probability of getting a card bearing a prime number less than 15 is `5/18`.
APPEARS IN
RELATED QUESTIONS
A die is thrown once. Find the probability of getting a number other than 3.
A child has a die whose 6 faces show the letters given below:
The die is thrown once. What is the probability of getting (i) A and (ii) B?
Two dice are rolled together. Find the probability of getting such numbers on two dice whose product is a perfect square.
A box contains 90 discs which are numbered from 1 to 90. If one disc is drawn at random from the box, find the probability that it bears a number divisible by 5.
There are 40 students in a class of whom 25 are girls and 15 are boys. The class teacher has to select one student as a class representative. He writes the name of each student on a separate card, the cards being identical. Then she puts cards in a bag and stirs them thoroughly. She then draws one card from the bag. What is the probability that the name written on the card is the name of a girl ?
One card is drawn from a well-shuffled deck of 52 cards. Find the probability of drawing a red king.
A box contains cards bearing numbers 6 to 70. If one card is drawn at random from the box, find the probability that it bears a one-digit number,
Two coins are tossed simultaneously. What is the probability of getting at most one head?
In a lottery, there are 6 prizes and 24 blanks. What is the probability of not getting a prize?
The probability of throwing a number greater than 2 with a fair die is
