Class 12

Math

Algebra

Probability I

In a n-sided regular polygon, the probability that the two diagonal chosen at random will intersect inside the polygon is

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India plays two matches each with West Indies and Australia. In any match the probabilities of India getting points $0,1and2$ are $0.45,0.05and0.50$ respectively. Assuming that the outcomes are independent, the probability of India getting at least 7 points is (a) $0.8750$ (b) $0.0875$ (c) $0.0625$ (d) $0.0250$

A pair of unbiased dice are rolled together till a sum of “either 5 or 7” is obtained. Then find the probability that 5 comes before 7.

A bag contains an assortment of blue and red balls. If two balls are drawn at random, the probability of drawing two red balls is five times the probability of drawing two blue balls. Furthermore, the probability of drawing one ball of each color is six time the probability of drawing two balls. The number of red and blue balls in the bag is $6,3$ b. $3,6$ c. $2,7$ d. none of these

An urn contains 3 red balls and $n$ white balls. Mr. A draws two balls together from the urn. The probability that they have the same color is 1/2 Mr. B. Draws one balls form the urn, notes its color and replaces it. He then draws a second ball from the urn and finds that both balls have the same color is 5/8. The possible value of $n$ is $9$ b. $6$ c. $5$ d. 1

A coin is tossed 7 times. Then the probability that at least 4 consecutive heads appear is $3/16$ b. $5/32$ c. $3/16$ d. $1/8$

Let $AandB$ b e two independent events. Statement 1: If $(A)=0.3andP(A∪B)=0.8,thenP(B)$ is 2/7. Statement 2: $P(E)=1−P(E),whereE$ is any event.

If $n$ persons are seated on a round table, what is the probability that two named individuals will be neighbours?

If $AandB$ are two independent events such that $P(A)=1/2andP(B)=1/5,$ then a.$P(A∪B)=3/5$ b. $P(A/B)=1/4$ c. $P(A/A∪B)=5/6$ d. $P(A∩B/A∪B)=0$