Question

Brady is a figure skater. He finds a few of the jumps he does to be difficult, but the rest are easy for him. He must include four jumps in his routine. He always makes the first jump a difficult one. After a difficult jump, there is a 0.3 probability that he'll do another difficult jump, and otherwise he'll do an easy one. After an easy jump, there is a 0.4 probability that he'll do another easy one, and otherwise he'll do a hard one.
What is the probability that the final jump of his routine will be an easy one ?
What is the probability that all four jumps of his routine will be difficult ones?

Answer 1

let D and E represent the event of difficult and easy jump

1)probability that the final jump of his routine will be an easy one

=P(DEEE)+P(DEDE)+P(DDEE)+P(DDDE)

=1*0.7*0.4*0.4+1*0.7*0.6*0.7+1*0.3*0.7*0.4+1*0.3*0.3*0.7

=0.553

2)

P( all four jumps of his routine will be difficult ones ) =P(DDDD) =1*0.3*0.3*0.3 =0.027