The Mathematics of Maybe: Introduction to Probability: CBSE Class 9 Mathematics practice questions

C. Subjective probability, a personal judgement based on the evidence they see

Estimates based on how a person reads the situation are subjective probability. Rain is not an equally likely two-outcome event, so the idea that "rain or no rain" must be $\dfrac{1}{2}$ is a common slip. Experimental and theoretical probability need repeated trials or equally likely outcomes, which neither friend used.

B. About $1000$ times

For a fair die $P(4) = \dfrac{1}{6}$, and in the long run the share of 4s gets close to this (the Law of Large Numbers). Expected count $= \dfrac{1}{6} \times 6000 = 1000$. Dividing 6000 by 4 gives $1500$, and $960$ would come from reusing the experimental $0.16$ from only 50 rolls.

A. $140$

$P(\text{yellow}) = \dfrac{7}{30}$, so the estimate is $\dfrac{7}{30} \times 600 = 140$. Using the blue count gives $\dfrac{5}{30} \times 600 = 100$, using red gives $200$, and dividing $600 \div 7 \approx 86$ ignores the sample size of 30.