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Slaybre8952
08.10.2020 •
Mathematics
A football team is known to run 30% of its plays to the left and 70% to the right. A linebacker on an opposing team notices that, when plays go to the right, the right guard shifts his stance most of the time (80%) and that he uses a balanced stance the remainder of the time. When plays go to the left, the guard takes a balanced stance 90% of the time and the shift stance the remaining 10%. On a particular play, the linebacker notes that the guard takes a balanced stance. (a) What is the probability that the play will go to the left
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Ответ:
0.6585
Step-by-step explanation:
Given the following :
Proportion of play to the left = 30% = 0.3
Proportion of play to the right = 70% = 0.7
Play to the right:
Shift stance = 80% = 0.8
Balanced stance = (1 - 0.8) = 0.2
Play to the right with balanced stance = (0.2 × 0.7) = 0.14
Play to the right with shifted stance = (0.8 × 0.7) = 0.56
Play to the left:
Balanced stance = 90% = 0.9
Shifted stance = (1 - 0.9) = 0.1
Play to the left with balanced stance = (0.9 × 0.3) = 0.27
Play to the left with shifted stance = (0.9 × 0.3) = 0.03
Probability that play will go to the left if the linebacker takes a balanced stance :
Overall proportion of play with balanced stance :
Balanced with play to the right + balanced with play to the left = (0.14 + 0.27) = 0.41
Balanced play to the left = 0.27
= (balanced play to the left / total proportion of balanced stance)
= 0.27 / 0.41
= 0.6585365
= 0.6585
Ответ:
i. Estimated number of free throws of the best player = 0.85 * 40
ii. 34 free throws
Step-by-step explanation:
Percentage of free throws made by the best player = 85%
Percentage of free throws made by the second best player = 75%
Percentage of free throws made by the third best player = 70%
Therefore, for 40 attempts;
i. Estimated number of free throws made by the best player = 85% x 40
= 0.85 x 40
= 34
ii. Estimated number of free throws made by the second best player = 75%x 40
= 0.75 x 40
= 30
iii. Estimated number of free throws made by the third best player = 70% x 40
= 0.70 x 40
= 28
Thus, the equation that gives the estimated number of free throws is 0.85 * 40.
The best player will make about 34 free throws.