Q2(ii):
Which of the following experiments have equally likely outcomes? Explain. (ii) A player attempts to shoot a basketball. She/he shoots or misses the shot.

Solution :

Given: An experiment where a player attempts to shoot a basketball, resulting in either a "shot" (success) or a "miss" (failure).

To Find: Determine whether the outcomes of this experiment are "equally likely" and provide a logical explanation.

Definition of Equally Likely Outcomes:
Outcomes of an experiment are said to be equally likely if each outcome has the same probability of occurring. If an experiment has $n$ outcomes, each outcome is equally likely if the probability of each is $\frac{1}{n}$.

Step 1: Identifying the Sample Space
Let $S$ be the sample space of the experiment.
The possible outcomes are:
$E_1$: The player shoots the ball (Success).
$E_2$: The player misses the shot (Failure).
Thus, $S = \{E_1, E_2\}$.

Step 2: Analyzing the Nature of the Experiment
The probability of a basketball player making or missing a shot depends on several factors, including:
1. The skill level of the player.
2. The distance from the basket.
3. The defensive pressure.
4. The physical and mental state of the player.

Step 3: Evaluating the Likelihood
Let $P(E_1)$ be the probability of shooting the ball successfully and $P(E_2)$ be the probability of missing the shot.
For the outcomes to be equally likely, we must have $P(E_1) = P(E_2) = 0.5$.
However, in a real-world scenario, a professional player has a high probability of success ($P(E_1) > 0.5$), while a novice player may have a low probability of success ($P(E_1) < 0.5$). Since the probability is dependent on the player's ability and external conditions, it is not fixed at $0.5$ for every player or every attempt.

Step 4: Conclusion
Since the probability of hitting the basket is not necessarily equal to the probability of missing the basket, the outcomes are not equally likely.

Final Answer: The outcomes are not equally likely because the probability of shooting or missing depends on the player's skill and various other factors, and is not inherently fixed at $50\%$ for each outcome.

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Q2(ii): Which of the following experiments have equally likely outcomes? Explain. (ii) A player attempts to shoot a basketball. She/he shoots or misses the shot.

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Q2(ii):
Which of the following experiments have equally likely outcomes? Explain. (ii) A player attempts to shoot a basketball. She/he shoots or misses the shot.