Maharashtra Board Class 10 Maths Chapter 5 Probability Set 5.1 Solutions

Question 1. How many possibilities are there in each of the following?
(i) Vanita knows the following sites in Maharashtra. She is planning to visit one of them in her summer vacation. Ajintha, Mahabaleshwar, Lonar Sarovar, Tadoba wild life sanctuary, Amboli, Raigad, Matheran, Anandavan.
(ii) Any day of a week is to be selected randomly.
(iii) Select one card from the pack of 52 cards.
(iv) One number from 10 to 20 is written on each card. Select one card randomly.
Answer:
(i) Here, 8 sites of Maharashtra are given.
∴ There are 8 possibilities in a random experiment of visiting a site out of 8 sites in Maharashtra.
(ii) There are 7 days in a week.
∴ There are 7 possibilities in a random experiment of selecting a day of the week.
(iii) There are 52 cards in a pack of cards.
∴ There are 52 possibilities in a random experiment of selecting one card from the pack of 52 cards.
(iv) There are 11 cards numbered from 10 to 20.
∴ There are 11 possibilities in a random experiment of selecting one card from the given set of cards.
In simple words: The number of possibilities corresponds to the total number of distinct items or choices available in each scenario, such as sites, days of the week, cards in a deck, or numbered cards.

🎯 Exam Tip: When asked for "possibilities," simply count the total number of unique outcomes or items that can be chosen or occur in the given experiment.

Question 1. In which of the following experiments possibility of expected outcome is more? (Textbook pg, no. 116)
(i) Getting 1 on the upper face when a die is thrown.
(ii) Getting head by tossing a coin.
Answer:
(i) On a die there are 6 numbers.
∴ There are 6 possibilities of getting any one number from 1 to 6 on the upper face i.e. \( \frac{1}{6} \) is the possibility.
(ii) There are two possibilities (H or T) on tossing a coin i.e. \( \frac{1}{2} \) possibility.
∴ In the second experiment, the possibility of expected outcome is more.
In simple words: The probability of getting a head on a coin toss (1/2) is higher than getting a specific number (like 1) on a die roll (1/6), meaning the coin toss has a greater possibility for its expected outcome.

🎯 Exam Tip: To compare possibilities, calculate the probability of the expected outcome for each experiment. The higher probability indicates a greater possibility.

Question 2. Throw a die, once. What are the different possibilities of getting dots on the upper face? (Textbook pg. no. 114)
Answer: There are six different possibilities of getting dots on the upper face. They are
ℹ️ चित्र व्याख्या (Diagram Explanation): यह चित्र एक मानक पासे के सभी छह संभावित मुखों को दर्शाता है, जिनमें प्रत्येक पर क्रमशः 1, 2, 3, 4, 5 और 6 बिंदु बने हुए हैं। यह बताता है कि एक पासा फेंकने पर कौन-कौन से परिणाम मिल सकते हैं।
In simple words: When a die is thrown once, the possible outcomes for the number of dots on the upper face are 1, 2, 3, 4, 5, or 6, representing six distinct possibilities.

🎯 Exam Tip: Remember that a standard die has six faces, each showing a unique number of dots from 1 to 6. Listing these directly provides all possible outcomes for a single throw.