Question

2. Caleb makes 70% of his free throws and is shooting free throws after practice. What is the
probability that
a) He makes the first free throw he shoots.
b) He does not make a free throw until his third attempt.
c) He does not make a free throw until his tenth attempt.
d) How many free throws should Caleb expect to shoot until he makes his first shot?

Answer 1

Answer:

shooting trough are 70 per cent

Answer 2

Answer:

a) 0.7

b) 0.063

c) 0.0000137781

d) If Caleb makes 100 shots, he may expect at maximum 70 free throws before first shot.

Step-by-step explanation:

Let E be the event ‘he makes first free throw he shoots’.

Clearly, P(F) = 70/100 = 0.7

Let F be the event ‘he does not make a free throw until his third attempt’.

P(F) = [1 – P(E)] [1 – P(E)] [P(E)]

= 0.3 × 0.3 × 0.7

= 0.063

Let G be the event ‘he does not make a free throw until his tenth attempt’.

P(G) = (0.3)⁹ × 0.7 = 0.0000137781

Hope it helps!

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