Probability Tes...

Given two mutually exclusive events $$A$$ and $$B$$ such that $$P(A)=\dfrac 12$$ and $$P(B)=\dfrac 13$$, find $$P(A\ or\ B)$$

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$$12$$ defective pens are accidentally mixed with $$132$$ good ones. It is not possible to just look at a pen and tell whether or not it is defective. One pen is taken out at random from this lot. Determine the probability that the pen taken out is a good one.

A card is picked at random from a pack of $$52$$ playing cards. given that the picked card is a queen, the probability of this card to be a card of spade is

A quadratic equation $$ax^2 + bx + c = 0$$, with distinct coefficients is formed. It a, b, c are chosen from the numbers $$2, 3, 5$$ then the probability that the equation has real roots is

Two dice of different colours are thrown at a time. The probability that the sum is either $$7$$ or $$11$$ is 

A coin is tossed $$5$$ times. What is the probability that tail appears an odd number of times?

If $$A$$ and$$B$$ are mutually exclusive events such that $$P(A)=0.4,P(B)=x$$ and $$P(A\cup B)=0.5$$, then $$x=$$?

In a class, $$60$$% of the students read mathematics, $$25$$% biology and $$15$$% both mathematics and biology. One student is selected at random. What is the probability that he reads mathematics, if it is known that he reads biology?

A fair coin is tossed $$6$$ times. What is the probability of getting at least $$3$$ heads?

A die is thrown twice and the sum of the numbers appearing is observed to be $$7$$. What is the conditional probability that the number $$2$$ has appeared at least once?