class 12

Math

Algebra

Probability

The minimum number of times a fair coin needs to be tossed, so that the probability of getting at least two heads is at least 0.96 is :

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A box contains 90 discs, numbered from 1 to 90. If one disc is drawn at random from the box,find the probability that it bears a prime number < 23.

A box has 20 pens of which 2 are defective. Calculate the probability that out of 5 pens drawn one by one with replacement, at most 2 are defective.

All kings, queens are aces are removed from a pack of 52 cards. The remaining cards are well shuffled and then a card is drawn from it. Find the probability that the drawn card is :a black face card (b) a red card.

A card from a pack of 52 playing cards is lost. From the remaining cards of the pack three cards are drawn at random (without replacement) and are found to be all spades. Find the probability of the lost card being a spade.

Let $E_{c}$ denote the complement of an event $E.$ Let $E,F,G$ be pairwise independent events with $P(G)>0$ and $P(E∩F∩G)=0$ Then $P(E_{c}∩F_{c}∩G)$ equals (A) $P(E_{c})+P(F_{c})$ (B) $P(E_{c})−P(F_{c})$ (C) $P(E_{c})−P(F)$ (D) $P(E)−P(F_{c})$

A card is drawn at random from a well shuffled pack of 52 playing cards. Find the probability of getting neither a red card nor a queen and (2) a face card

Suppose a girl throws a die. If she gets 1 or 2 , she tosses a coin three times and notes the number of tails. If she gets 3,4,5 or 6, she tosses the coin once and notes whether 'head' or 'tail' is obtained. If she obtained exactly one 'tail', what is the probability that she threw 3,4,5,or 6 with the die

Cards bearing numbers 1, 3, 5,.....,35 are kept in a bag. A card is drawnat random from the bag. Find the probability of getting a card bearing(i) a prime number less than 15.(ii) a number divisible by 3 and 5.