Important Questions for Class 10 Chapter 15 - Probability

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Important questions based on NCERT syllabus for Class 10 Chapter 15 - Probability:

Question 1: A bag contains red, blue and green balls. It is twice as likely to pick a blue ball as compared to a red ball, and it is thrice as likely to pick a green ball as compared to a red ball. What is the probability of picking a green ball?
Solution:

Let P (Red) = x
Then, P (Blue) = 2x and P (Green) = 3x
x + 2x + 3x = 1 (Because the sum of probabilities of all outcomes is 1)
x = 16.
P (Green) = 3/6 = ½ .

Question 2: A dice is thrown twice. Find the probability of getting a bigger value on the first throw.
Solution:
There are 36 outcomes for rolling a die twice.
Let us first consider the event “Getting the same value” for rolling a die twice. There are 6 favourable outcomes, so the probability is 6/36.

So, the probability of getting different values on rolling a die twice is 1 - 6/36 = 30/36

Of these, getting a bigger value on the first and getting a bigger value on the second are equally likely.

Hence, both these probabilities = 12×30/36=15/36

Question 3: Two die are thrown simultaneously. How many outcomes are possible for the sum of the values? Are these outcomes equally likely? Explain.
Solution:
There are 36 equally likely outcomes for the ordered pair showing the two values obtained on the two dice, but as far as the sum of these values is concerned, there are only 11 possible outcomes: 2, 3, 4, … 12.

Each of these 11 outcomes has 1 or more outcomes from the first case mapped to it.
For example, the sum of 2 is only possible when we get (1, 1)

But a sum of 7 is obtained in 6 cases [(6,1) (1,6) (5,2) (2,5) (3,4) (4,3)] of the 36 outcomes which are not same as obtaining 2 as the sum.

Hence, the 11 outcomes for the sum of values are not equally likely.