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QUESTION: 1

Five marbles are drawn from a bag which contains 6 blue marbles and 7 green marbles. Then, the probability that 3 will be blue and 2 green is:

Solution:

Blue = 6

Green = 7

Number of ways 3 blue marbles can be drawn = ^{6}C_{3}

number of ways 2 green marbles can be drawn = _{7}C_{2}

total ways of drawing 5 marbles = ^{13}C_{5}

=> probability = (^{6}C_{3} * ^{7}C_{2})/^{13}C_{5}

= 140/429

QUESTION: 2

A four digit number is formed by using the digits 1,2,3,4,5,6,7 without repetition. What is the probability that it’s divisible by 2?

Solution:

QUESTION: 3

One card is drawn from a well shuffled pack of 52 cards. If each outcome is equally likely, what is the probability that the card will be a red card?

Solution:

QUESTION: 4

The probability that the birth days of six different persons will fall in exactly two calendar months is:

Solution:

QUESTION: 5

An urn contains 9 red, 7 white and 4 black balls. If two balls are drawn at random, then the probability that one ball is white is:

Solution:

n(S) = 20C^{2}

= P^{2} = (7C1 ⋅ 13C1)/20C^{2}

= 91/190

QUESTION: 6

One card is drawn from a well shuffled pack of 52 cards. If each outcome is equally likely, what is the probability that the card will not be a red card?

Solution:

QUESTION: 7

The odds in favour of an event are 6 : 5. The probability of occurrence of this event:

Solution:

QUESTION: 8

When two dice are thrown what’s the probability of getting a sum less than 4?

Solution:

QUESTION: 9

A coin is tossed twice. What is the probability that atleast one tail occurs?

Solution:

QUESTION: 10

A coin is tossed. If head comes up a die is thrown but if tail comes up, the coin is tossed again. The probability of obtaining head and number 6 is:

Solution:

Required sample space is {H1, H2, H3, H4, H5, H6, TH, TT}

∴ P(S) = 1/8

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