Class 12

Math

Algebra

Probability I

A box contains 6 nails and 10 nuts. Half of the nails and half of the nuts are rusted. If one item is chosen at random, then find the probability that it is rusted or is a nail.

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The probability that a student is not a swimmer is $51 $ . Then the probability that out of five students, four are swimmers is (A) $_{5}C_{4}(54 )_{4}51 $ (B) $(54 )_{4}51 $ (C) $_{5}C_{1}51 (54 )_{4}$ (D) None of these

The probability of happening an event A in one trial is 0.4. Find the probability that the event A happens at least one in three independent trials.

If two events $AandB$ are such that $P(A_{c})=0.3,P(B)=0.4,andP(A∩B_{c})=0.5$ , then find the value of $P[B/(A∪B_{c})]˙$

A box contains 5 red marbles, 8 white marbles and 4 green marbles. One marble is taken out of the box at random. What is the probability that the marble taken out will be(i) red ? (ii) white ? (iii) not green?

A bag contains 10 mangoes out of which 4 are rotten. Two mangoes are taken out together. If one of them is found to be good, the probability that other is also good is (a) $31 $ (b) $158 $ (c) $185 $ (d) $32 $

Two coins (a one rupee coin and a two rupee coin) are tossed once. Find a sample space.

One of 10 keys open the door. If we try the keys one after another, then find the following: (i) The probability that the door is opened on the first attempt. (ii) The probability that the door is opened on the second attempt. (iii) The probability that the door is opened on the 10th attempt.

A box contains 90 discs which are numbered from 1 to 90. If one disc is drawn at random from the box, find the probability that it bears (i) a two-digit number (ii) a perfect square number(iii) a number divisible by 5.