NCERT Solutions Class 9 Maths Chapter 15 — Probability

Solution:

Step 1: Experimental probability is calculated from actual experiments or observations.

Step 2: It is defined as the ratio of the number of times an event occurs to the total number of trials conducted.

Step 3: Therefore, P(E) = (Number of times E happened) / (Total number of trials).

Solution:

Step 1: The probability of any event E, denoted as P(E), must always satisfy the condition 0 ≤ P(E) ≤ 1.

Step 2: This means probability can be 0 (impossible event), 1 (certain event), or any fraction or decimal between 0 and 1.

Step 3: Values like 0.7, 1/2 (which is 0.5), and 0 all fall within this valid range.

Step 4: However, 1.5 is greater than 1, so it cannot be a valid probability for any event.

Solution:

Step 1: For any event E, the event 'not E' (also called the complementary event, E') represents all outcomes where E does not occur.

Step 2: The sum of the probabilities of an event and its complement is always 1, meaning P(E) + P(not E) = 1.

Step 3: From this relationship, we can find the probability of 'not E' by rearranging the equation.

Step 4: Therefore, P(not E) = 1 - P(E).

Solution:

Step 1: The total number of trials (coin tosses) is given as 200.

Step 2: The number of times the event 'getting a Head' occurred is 110.

Step 3: The experimental probability P(Head) = (Number of Heads) / (Total number of tosses).

Step 4: P(Head) = 110 / 200 = 11 / 20.

Solution:

Step 1: The total number of trials (die rolls) is 300.

Step 2: The outcomes that are greater than 4 are 5 and 6.

Step 3: The frequency of outcome 5 is 40. The frequency of outcome 6 is 50.

Step 4: The total number of times 'getting an outcome greater than 4' occurred = Frequency(5) + Frequency(6) = 40 + 50 = 90.

Step 5: Experimental probability P(outcome > 4) = (Number of times outcome > 4 occurred) / (Total number of trials) = 90 / 300.

Step 6: Simplifying the fraction: 90/300 = 9/30 = 3/10.