A certain weightlifter is prone to back injury. He finds that he has a 20% chance of hurting his back if he uses the proper form of bending at the hips and keeping his spine locked. The probability that he will hurt his back with bad form is 95%. The probability that he uses proper form is 75%. What is the probability he hurts his back

Question

Mathematics

Kibbles

17 April, 13:09

A certain weightlifter is prone to back injury. He finds that he has a 20% chance of hurting his back if he uses the proper form of bending at the hips and keeping his spine locked. The probability that he will hurt his back with bad form is 95%. The probability that he uses proper form is 75%. What is the probability he hurts his back

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Scarlett Collier · Answer 1

Probability weightlifter hurts his back = 0.3875 i. e 38.75%

Step-by-step explanation:

Probability of using right body form = 75%

Probability of using bad body form : 1 - Prob (right body form) = 1 - 75% = 25%

Probability of getting injured if right body form = 20%

Probability of getting injured if using bad body form = 95%

Probability of getting injury:

Prob (Right body form & injury) or Prob (wrong body firm & injury)

(0.75) (0.20) + (0.25) (0.95)

0.15 + 0.2375

= 0.3875 i. e 38.75%