Question

3. The probability of a marksman scoring a bulls-eye on any shot is 0.26. The probability
of an inner is 0.42 and the probability of an outer is 0.24. What is the probability of each of

the following:
a) Scoring an inner or better. This means an inner or closer.
b) Failing to hit the target.
c) Failing to score a bulls-eye.

Answer 1

Answer:

a) 0.68

b) 0.08

c) 0.74

Step-by-step explanation:

Given that:

Probability of hitting bulls eye, P(B) = 0.26

Probability of an inner, P(I) = 0.42

Probability of an outer, P(O) = 0.24

a) Probability of hitting an inner or better (inner or bulls eye):

P(I or B) = P(I $\cup$ B)

Formula for P(P $\cup$ Q)  where P(P) and P(Q) are the probabilities of two mutually exclusive events i.e. having nothing in common:

P(P $\cup$ Q)  = P(P) + P(Q)

P(I $\cup$ B)  = P(I) + P(B) = 0.26 + 0.42 = 0.68

b) Probability of failing to hit the target:

P(F) = 1 - (P(B)+P(I)+P(O))

P(F) = 1 - (0.26 + 0.42 + 0.24)) = 1 - 0.92 = 0.08

c) Probability of failing to score a bulls eye:

P(B)' = 1 - P(B) = 1 - 0.26  = 0.74

So, the answers are:

a) 0.68

b) 0.08

c) 0.74