Question

The probability that ramu will pass the examination in both mathematics and physics is 0.5, the probability of passing neither mathematics nor physics is 0.1 the probability of passing mathematics is 0.75.

a.What is the probability of passing mathematics or physics? (1)

b.What is probability of passing physics? (3)

Answer 1

Given : The probability that ramu will pa ss the examination in both mathematics and physics is 0.5,

the probability of pa ssing neither mathematics nor physics is 0.1

the probability of pa ssing mathematics is 0.75.

To Find :

a. What is the probability of pa ssing mathematics or physics? (1)

b. What is probability of pa ssing physics? (3)

Solution:

probability that ramu will pa ss the examination in both mathematics and physics is 0.5,

P ( M  ∩ P ) = 0.5

P ( M' ∩ P') = 0.1

De Morgan Law :  $\[P\left( A'\text{ }\cup \text{ }B' \right)=P\left( A\cap B \right)\text{ }\!\!'\!\!\text{ },\text{ }P\left( A'\text{ }\cap \text{ }B' \right)=P\left( A\cup B \right)\text{ }\!\!'\!\!\text{ }\]$

P ( M' ∩ P') = 0.1

=> P ( M ∪ P)' = 0.1

=> P ( M U P ) = 1 - 0. 1 = 0.9

probability of pa ssing mathematics or physics =   0.9

probability of pa ssing physics

P ( M U P ) = P(M ) + P (P)  - P ( M  ∩ P )  

=>  0.9  = 0.75 +  P (P)  - 0.5

=>  P (P)  = 0.65

probability of pa ssing physics   = 0.65

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