Suppose that a netball player has a probability of 1/2 of scoring a goal each time. What is the
probability that she will score one goal from her first two attempts ?
Correct answer is '0.5'. Can you explain this answer?

Question

Suppose that a netball player has a probability of 1/2 of scoring a goal each time. What is the
probability that she will score one goal from her first two attempts ?

Correct answer is '0.5'. Can you explain this answer?

Answer

Probability of scoring a goal:
- The netball player has a probability of 1/2 of scoring a goal each time she attempts a shot.

Finding the probability of scoring one goal from the first two attempts:
- To find the probability that she will score one goal from her first two attempts, we need to consider the possible outcomes.
- There are three scenarios in which she can score one goal:
1. She scores on her first attempt but misses on her second.
2. She misses on her first attempt but scores on her second.
3. She scores on both attempts.

Calculating the probability:
- The probability of scoring on the first attempt and missing on the second is (1/2) * (1/2) = 1/4.
- The probability of missing on the first attempt and scoring on the second is (1/2) * (1/2) = 1/4.
- The probability of scoring on both attempts is (1/2) * (1/2) = 1/4.

- Therefore, the total probability of scoring one goal from the first two attempts is 1/4 + 1/4 = 1/2, which is equal to 0.5.

Therefore, the correct answer is 0.5, indicating that there is a 50% chance that the netball player will score one goal from her first two attempts.

Answer

If the player scores one goal from her first two attempts, then the sequence of events could be either a goal first (G) followed by a miss (M) or a miss first (M) followed by a goal (G). Thus : Pr(one goal from first two attempts) = Pr(GM) + Pr(MG)

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