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Probability

Short Answer Type

331.

A box has cards numbered 14 to 99. Cards are mixed throughly and a card is drawn from the bag at random. Find the probability that the number on the card drawn from the box is

(i)    an odd number.
(ii)    a perfect square number.
(iii)    an number divisible by 7.

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332.

A card is drawn at random from a well -shuffled fled pack of 52 playing cards. Find the probability of getting neither a red card nor a queen.

3046 Views

333.

Three different coins are tossed together. Find the probability of getting
(i) exactly two heads
(ii) at least two heads
(iii) at least two tails.

2481 Views

334.

A number x is selected at random from the numbers 1, 2, 3, and 4. Another number y is selected at random from the numbers 1, 4, 9 and 16. Find the probability that product of x and y is less than 16.

6232 Views

335.

The different dice are tossed together. Find the probability that the product of the two number on the top of the dice is 6.

2773 Views

336. The probability of selecting a red ball at random from a jar that contains only red, blue and orange balls is 1/4. The probability of selecting a blue ball at random from the same jar is 1/3. If the jar contains 10 orange balls, find the total number of balls in the jar.

1336 Views

Long Answer Type

337. A card is drawn at random from a well-shuffled deck of playing cards.

(i) a card of a spade or an ace.
(ii) a black king
(iii) neither a jack nor a king
(iv) either a king or queen

882 Views

Short Answer Type

338.

A number is chosen at random from the number –3, –2, –1, 0, 1, 2, 3. What will be the probability that square of this number is less then or equal to 1?

3719 Views

339.

Two different dice are thrown together. Find the probability that the numbers obtained
(i) have a sum less than 7
(ii) have a product less than 16
(iii) is a doublet of odd numbers.

9211 Views

Long Answer Type

340.
Peter throws two different dice together and finds the product of the two numbers obtained. Rina throws a die and squares the number obtained. Who has the better chance to get the number 25.

Let us first write the all possible oucomes when Peter throws two different dice together.

(1,1), (1,2), (1,3), (1,4), (1,5), (1,6)
(2,1), (2,2), (2,3), (2,4), (2,5), (2,6)
(3,1), (3,2), (3,3), (3,4), (3,5), (3,6)
(4,1), (4,2), (4,3), (4,4), (4,5), (4,6)
(5,1), (5,2), (5,3), (5,4), (5,5), (5,6)
(6,1), (6,2), (6,3), (6,4), (6,5), (6,6)

∴ Total number of outcomes = 36

The favorable outcome for getting the product of numbers on the dice equal to 25 is (5, 5).

Favourable number of outcomes = 1

∴ Probability that Peter gets the product of numbers as 25
= $fraction numerator Favourable space number space of space outcomes over denominator Total space number space of space outcomes end fraction space equals space 1 over 36$

The outcomes when Rina throws a die are 1, 2, 3, 4, 5, 6.

∴ Total number of outcomes = 6

Rina throws a die and squares the number, so to get the number 25, the favourable outcome is 5.

Favourable number of outcomes = 1

∴ Probability that Rina gets the square of the number as 25
$fraction numerator Favourable space number space of space outcomes over denominator Total space number space of space outcomes end fraction space equals fraction numerator space 1 over denominator 6 end fraction$
As, 1/6>1/36, so Rina has better chance to get the number 25.