NCERT Solutions Class 10 Maths Chapter 14 — Probability

Solution:

Step 1: The probability of any event E, denoted as P(E), must be a value between 0 and 1, inclusive.

Step 2: P(E) = 0 means the event is impossible, and P(E) = 1 means the event is certain.

Step 3: Therefore, the statement 0 ≤ P(E) ≤ 1 is always true for any event.

Solution:

Step 1: The total number of possible outcomes when rolling a fair die is {1, 2, 3, 4, 5, 6}, so Total Outcomes = 6.

Step 2: The favorable outcomes for getting an even number are {2, 4, 6}, so Favorable Outcomes = 3.

Step 3: The probability of getting an even number is (Favorable Outcomes) / (Total Outcomes) = 3/6 = 1/2.

Solution:

Step 1: The probability of any event must be a value between 0 and 1, inclusive (0 ≤ P(E) ≤ 1).

Step 2: A negative probability value is not possible for any event, nor can it be greater than 1.

Step 3: Therefore, the student's calculation resulting in -0.5 is incorrect.

Solution:

Step 1: For Event A: The maximum sum possible when rolling two fair dice is 6 + 6 = 12. Therefore, getting a sum of 13 is an impossible event, so P(A) = 0.

Step 2: For Event B: When rolling a single fair die, the possible outcomes are {1, 2, 3, 4, 5, 6}. All these numbers are less than 7. Therefore, getting a number less than 7 is a sure event, so P(B) = 1.

Step 3: Thus, A is an impossible event and B is a sure event.

Solution:

Step 1: Total number of balls in the bag = 3 (red) + 5 (black) + 2 (white) = 10 balls.

Step 2: Number of balls that are NOT black = Number of red balls + Number of white balls = 3 + 2 = 5 balls.

Step 3: The probability of drawing a ball that is NOT black = (Number of non-black balls) / (Total number of balls) = 5/10 = 1/2.