7.6 Probability, Long Questions (Question 1)


Question 1:
Peter, William and Roger compete with each other in shooting a target. The probabilities that they strike the target are 2 5 , 3 4  and  2 3  respectively. Calculate the probability that
(a) all the three of them strike the target,
(b) only one of them strikes the target,
(c) at least one of them strikes the target.

Solution:
Let S = Strike and M = Missed
Probability of Peter missed the target= 3 5 Probability of William missed the target= 1 4 Probability of Roger missed the target= 1 3



(a)
Probability (all three persons strike the target) = 2 5 × 3 4 × 2 3 = 1 5

(b)
Probability (only one of them strikes the target) =P( only Peter struck )+P( only William struck )+P( only Roger struck ) =( 2 5 × 1 4 × 1 3 )+( 3 5 × 3 4 × 1 3 )+( 3 5 × 1 4 × 2 3 ) = 1 30 + 3 20 + 1 10 = 17 60

(c)
Probability (at least one of them strikes the target) =1P(all missed the target) =1( 3 5 × 1 4 × 1 3 ) =1 1 20 = 19 20