Exam-style CBSE practice questions on Theoretical Probability (The Mathematics of Maybe: Introduction to Probability). Try each one first, then reveal the correct answer and a step-by-step explanation. Free, from EduLevel — the AI teacher for CBSE.
A fair die is rolled once. The probability of getting an even number is:
Explanation: A fair die has 6 equally likely outcomes: 1, 2, 3, 4, 5, 6. The even numbers are 2, 4 and 6, giving 3 favourable outcomes. P(even) = 3/6 = 1/2.
When two fair coins are tossed together, the total number of outcomes in the sample space is:
Explanation: Each coin can land in 2 ways, head or tail, so the total outcomes = 2 × 2 = 4. The sample space is HH, HT, TH, TT. Note that HT and TH are different outcomes, so the answer is 4, not 3.
A bag contains 3 red balls and 5 black balls. One ball is drawn at random. The probability that it is red is:
Explanation: Total balls = 3 + 5 = 8, and each ball is equally likely to be drawn. Favourable outcomes (red balls) = 3. P(red) = 3/8. Writing 3/5 compares red with black instead of red with the total.
The probability that it will rain in Mumbai tomorrow is 0.85. The probability that it will NOT rain tomorrow is:
Explanation: Raining and not raining are complementary events, so their probabilities add up to 1. P(no rain) = 1 − 0.85 = 0.15.
In a dice game, two fair dice are thrown together. The probability of getting a total of 7 is:
Explanation: When two dice are thrown, the total number of outcomes = 6 × 6 = 36. The pairs giving a sum of 7 are (1,6), (2,5), (3,4), (4,3), (5,2) and (6,1), which is 6 outcomes. P(sum 7) = 6/36 = 1/6.
One card is drawn from a well-shuffled deck of 52 cards. The probability of getting a red face card is:
Explanation: A deck has 12 face cards (jacks, queens and kings), of which 6 are red, coming from hearts and diamonds. P(red face card) = 6/52 = 3/26. Taking all 12 face cards gives 12/52 = 3/13, which ignores the colour condition.
A bag contains 4 red, 3 blue and 5 green balls. One ball is drawn at random. The probability that it is NOT green is:
Explanation: Total balls = 4 + 3 + 5 = 12. Balls that are not green = 4 red + 3 blue = 7. P(not green) = 7/12. This is the same as 1 − P(green) = 1 − 5/12 = 7/12.
Three fair coins are tossed together. The probability of getting exactly two heads is:
Explanation: Three coins give 2 × 2 × 2 = 8 equally likely outcomes. Exactly two heads occurs in HHT, HTH and THH, which is 3 outcomes. P(exactly two heads) = 3/8.
At a school fete, tickets numbered 1 to 20 are mixed thoroughly and one ticket is drawn at random. The probability that the ticket bears a number which is a multiple of 3 or a multiple of 7 is:
Explanation: Multiples of 3 from 1 to 20 are 3, 6, 9, 12, 15, 18, which is 6 numbers, and multiples of 7 are 7 and 14, which is 2 numbers. No number up to 20 is a multiple of both 3 and 7, since 21 is greater than 20, so favourable outcomes = 6 + 2 = 8. P = 8/20 = 2/5.
Two fair dice are thrown together. The probability that the product of the two numbers on top is 12 is:
Explanation: Total outcomes = 6 × 6 = 36. The product is 12 for the pairs (2,6), (6,2), (3,4) and (4,3), which is 4 outcomes. P(product 12) = 4/36 = 1/9.
A bag contains 5 red balls and some blue balls. If the probability of drawing a blue ball at random is double the probability of drawing a red ball, the number of blue balls in the bag is:
Explanation: Let the number of blue balls be x, so the total is 5 + x. P(blue) = x/(5 + x) and P(red) = 5/(5 + x). Since P(blue) = 2 × P(red), we get x/(5 + x) = 10/(5 + x), so x = 10. Check: P(blue) = 10/15 = 2/3, which is exactly double P(red) = 5/15 = 1/3.
One card is drawn from a well-shuffled deck of 52 cards. The probability that the card is neither a red card nor a queen is:
Explanation: There are 26 red cards and 4 queens, but the 2 red queens get counted twice, so cards that are red or a queen = 26 + 4 − 2 = 28. Cards that are neither = 52 − 28 = 24. P = 24/52 = 6/13.
Stuck on a doubt in Theoretical Probability? Vidya ma'am — EduLevel's AI teacher — explains it to you live, by voice, till it clicks.
Try EduLevel free₹1 trial for 3 days · then ₹499/month · Get the Android app
