Maharashtra Board Class 10 Maths Chapter 5 Probability Set 5.2 Solutions

Question 1. For each of the following experiments write sample space 'S' and number of sample Point n(S)
(i) One coin and one die are thrown simultaneously.
(ii) Two digit numbers are formed using digits 2,3 and 5 without repeating a digit.
Answer:
(i) Sample space,
S = {(H, 1), (H, 2), (H, 3), (H, 4), (H, 5), (H, 6), (T, 1), (T, 2), (T, 3), (T, 4), (T, 5), (T, 6)}
∴ n(S) = 12
(ii) Sample space,
S = {23,25,32, 35, 52, 53}
∴ n(S) = 6
In simple words: A sample space lists all possible outcomes of an experiment, and n(S) is the count of these outcomes. For a coin and a die, it's combinations of Head/Tail with numbers 1-6. For two-digit numbers from 2,3,5 without repetition, it's all unique permutations like 23, 25, 32, etc.

🎯 Exam Tip: Remember to systematically list all possible outcomes for 'S' and then accurately count them for 'n(S)'. Pay close attention to conditions like "without repeating a digit".

Question 2. The arrow is rotated and it stops randomly on the disc. Find out on which colour it may stop.
ℹ️ चित्र व्याख्या (Diagram Explanation): एक गोलाकार डिस्क को छह बराबर क्षेत्रों में विभाजित किया गया है, प्रत्येक को अलग-अलग रंग दिया गया है: लाल, नारंगी, पीला, हरा, नीला और बैंगनी। केंद्र में एक तीर लगा हुआ है, जो घूमने के लिए स्वतंत्र है।
Answer:
There are total six colours on the disc.
Sample space,
S = {Red, Orange, Yellow, Blue, Green, Purple}
∴ n(S) = 6
∴ Arrow may stop on any one of the six colours.
In simple words: The sample space for this experiment is the set of all six colors on the disc. Since there are six distinct colors, the arrow has an equal chance of stopping on any one of them.

🎯 Exam Tip: When dealing with spinners or discs, the sample space consists of all distinct sections or outcomes available. Ensure all possibilities are listed for an accurate n(S) count.

Question 3. In the month of March 2019, find the days on which the date is a multiple of 5. (see the given page of the calendar).
Answer:

MARCH-2019

Dates which are multiple of 5:
5,10, 15,20,25,30
∴ S = {Tuesday, Sunday, Friday, Wednesday, Monday, Saturday}
∴ n(S) = 6
∴ The days on which the date will be a multiple of 5 are Tuesday, Sunday, Friday, Wednesday, Monday and Saturday.
In simple words: To find the days that are multiples of 5, locate the dates 5, 10, 15, 20, 25, and 30 on the calendar and then identify the corresponding days of the week for each date.

🎯 Exam Tip: Always carefully read the calendar and ensure all dates satisfying the given condition are selected. Double-check the corresponding day of the week for each selected date.

Question 4. Form a 'Road safety committee' of two, from 2 boys (B1 B2) and 2 girls (G1, G2). Complete the following activity to write the sample space.
Answer:
(i) Committee of 2 boys = B₁B₂
(ii) Committee of 2 girls = G₁G₂
(iii) Committee of one boy and one girl
= B₁G₁, B₁G₂, B₂G₁, B₂G₂
Sample space
= {B₁B₂, G₁G₂, B₁G₁, B₁G₂, B₂G₁, B₂G₂}
In simple words: To form a committee of two from two boys (B1, B2) and two girls (G1, G2), we list all combinations: two boys, two girls, or one boy and one girl. The sample space is the union of all these distinct pairs.

🎯 Exam Tip: When forming committees, ensure all unique combinations are considered for each category (e.g., all boys, all girls, boy-girl pairs). Systematic listing helps avoid omissions or repetitions.

Question 1. Sample Space
Answer:
• The set of all possible outcomes of a random experiment is called sample space.
• It is denoted by 'S' or 'Ω' (omega).
• Each element of a sample space is called a sample point.
• The number of elements in the set S is denoted by n(S).
• If n(S) is finite, then the sample space is called a finite sample space.

Some examples of finite sample space. (Textbook pg. no, 117)

In simple words: Sample space is the set of all possible outcomes of a random experiment, denoted by 'S' or 'Ω', with n(S) being the count of these outcomes. If n(S) is finite, it's a finite sample space. The table illustrates various common experiments and their corresponding sample spaces.

🎯 Exam Tip: Memorize the standard sample spaces and their sizes for common experiments like coin tosses, dice rolls, and card draws, as these are fundamental to probability problems. Understand that each outcome in the sample space is called a sample point.