Question

Sarah and thomas are going bowling. the probability that sarah scores more than 175 is 0.4, and the probability that thomas scores more than 175 is 0.2. their scores are independent. (a) find the probability that both score more than 175 (b) given that thomas score more than 175, the probability that sarah scores higher than thomas is 0.3. find the probability that thomas scores more than 175 and sarah scores higher than thomas

Answer 1

When the occurrence of one event say A does not affect the occurrence of another event say B, than the two events are said to be independent such that;

$\\   P(A\cap B)=P(A)\times P(B)$

where, P(A) = probability of occurrence of event A

and P(B) = probability of occurrence of event B

(a).

Now, let event A = Sarah scores more than 175

and event B = Thomas scores more than 175

Thus, P(A)= Probability that Sarah scores more than 175 = 0.4

and P(B)= Probability that Thomas scores more than 175 = 0.2

Since, the scores are independent, thus the probability that both Sarah and Thomas scores more than 175 is,

$\\   P(A\cap B)=P(A)\times P(B)\\   P(A\cap B)= 0.4\times 0.2= 0.08$

Hence, the required probability is 0.08

(b).

When the occurrence of one event say A affects the occurrence of another event say B, than the two events are said to be dependent such that;

$\\   P(A\cap B)=P(A)\times P(B\setminus A)$

Now, let event A = Sarah scores more than 175

and event B = Thomas scores more than 175

Thus, P(A)= Probability that Sarah scores more than 175 = 0.4

         P(B)= Probability that Thomas scores more than 175 = 0.2

and P(B|A) = Sarah scores more than Thomas given that Thomas scores more than 175 = 0.3

Thus, the required probability is calculated as follows;

$\\   P(A\cap B)=P(A)\times P(B\setminus A)\\   P(A\cap B)=0.2\times 0.3=0.06$