Probability: CBSE Class 10 Mathematics practice questions

B. $\dfrac{1}{2}$

A fair coin has two equally likely outcomes, head and tail, and one of them is a head, so $P(\text{head}) = \dfrac{1}{2}$. Wrong choices come from slips such as counting the edge as a third outcome ($\tfrac{1}{3}$), thinking a head is certain ($1$), or confusing it with two coins ($\tfrac{1}{4}$).

A. The outcomes "a red ball" and "a blue ball" are not equally likely, because there are more red balls

There are 5 balls and each ball is equally likely to be drawn, but the colours are not: 4 balls are red and only 1 is blue, so red is more likely. Having two colours does not make them equally likely, and the size of the balls only ensures each ball has the same chance. This is why not every experiment has equally likely outcomes.

D. $\dfrac{1}{4}$

After the queen is set aside, $4$ cards remain and exactly one is the ace, so $P = \dfrac{1}{4}$. Using $\tfrac{1}{5}$ forgets that the total has fallen to $4$, $\tfrac{1}{3}$ miscounts the cards left, and $\tfrac{3}{4}$ is $P(\text{not an ace})$.