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;

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

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3 years ago