Question

9. Marry plays a game of throwing a ball at a target.

The table shows information about the probability of each possible score.
0
1
*
2
3
4
Score
0.09
Probability
X
3x
0.16
0.21
Marry is three times more likely to score 2 points than to score 1 point.
a) Work out the value of x.
b) Mary plays the game twice.
Work out the probability of Mary scoring a total of 8.
5
0.30
6.......

Answer 1

6.97%

Explanation:

a) To work out the value of x, we can use the information given that "Marry is three times more likely to score 2 points than to score 1 point". We know that the probability of scoring 1 point is x, and the probability of scoring 2 points is 3x.

So we can set up the equation:

3x = probability of scoring 2 points

x = probability of scoring 1 point

We know that 3x = probability of scoring 2 points = 0.16

So we can solve for x by dividing both sides by 3:

x = 0.16 / 3 = 0.05333

b) To work out the probability of Mary scoring a total of 8, we can use the information from the table and the formula for the probability of a specific outcome when playing the game twice.

We know that the probability of scoring 4 points in one game is 0.21, so the probability of scoring 4 points twice is (0.21)^2 = 0.0441

We also know that the probability of scoring 2 points in one game is 3x = 3(0.05333) = 0.16, so the probability of scoring 2 points twice is (0.16)^2 = 0.0256

We can add these probabilities together to find the total probability of scoring 8 points:

0.0441 + 0.0256 = 0.0697 or 6.97%

So the probability of Mary scoring a total of 8 is 6.97%.