Class 12

Math

Algebra

Probability I

If p and q are chosen randomly from the set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} with replacement then determine the probability that the roots of the equation $x_{2}+px+q=0$ are real.

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In a musical chair game, the person playing the music has been advised to stop playing the music at any time within 2 minutes after she starts playing. What is the probability that the music will stop within the first half-minute after starting?

Fill in the blanks m following table: $P(A)$ $P(B)$ $(A∩B)$ $P(A∪B)$(i) $31 $ $51 $ $151 $ . . . (ii) 0.35 . . . 0.25 0.6(iii) 0.5 0.35 . . . 0.7

An urn contains 6 white and 4 black balls. A fair die is rolled and that number of balls we chosen from the urn. Find the probability that the balls selected are white.

Two dice are thrown. What is the probability that the sum of the numbers appearing on the two dice is 11, it 5 appears on the first?

A number is selected at random from the first 25 natural numbers. If it is a composite number, then it is divided by 6. But if it is not a composite number, it is divided by 2. Find the probability that there will be no remainder in the division.

A fair coin is tossed four times, and people win Re 1 for each head and lose Rs 1.50 for each tail that turns up. From the sample space calculate how many different amounts of money you can have after four tosses and the probability' of having each of these amounts.

Determine $P (E∣F)$ in : A coin is tossed three times, where (i) E : Head on third toss, F : heads on first two tosses (ii) E : at least two heads, F : at most two heads (iii) E : at most two tails, F : at least one tail

Events E and F are such that $P(¬Eor¬F)=0.25$, State whether E and F are mutually exclusive.