Class 12

Math

Algebra

Probability I

Three integers are chosen at random from the set of first 20 natural numbers. The chance that their product is a multiple of 3 is

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Find the probability that a leap year will have 53 Friday or 53 Saturdays.

A die is rolled. Let E be the event “die shows 4” and F be the event “die shows even number”. Are E and F mutually exclusive?

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

A die is thrown. Describe the following events:(i) A : a number less than 7 (ii) B : a number greater than 7(iii) C : a multiple of 3 (iv) D : a number less than 4(v) E : a even number greater than 4(vi) F : a number not less than 3 Also find \displaystyle{A}

A bag contains $n+1$ coins. If is known that one of these coins shows heads on both sides, whereas the other coins are fair. One coin is selected at random and tossed. If the probability that toss results in heads is 7/12, then find the value of $n˙$

A coin is tossed three times, consider the following events.A : ‘No head appears’, B: ‘Exactly one head appears’ and C: ‘Atleast two appear’.Do they form a set of mutually exclusive and exhaustive events?

A bag contains 9 discs of which 4 are red. 3 are blue and 2 are yellow. The discs are similar in shape and size. A disc is drawn at random from the bag.Calculate the probability that it will be (i) red. (ii) yellow, (iii) blue, (iv) not blue,(v) either red or yellow.

Consider the experiment in which a coin is tossed repeatedly until a head comes up. Describe the sample space.