The probability of this card being a king or a jack.

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If a card is drawn from a well-shuffled pack of 52 playing cards, then the probability of this card being a king or a jack is
(a) \\ \frac { 1 }{ 26 }
(b) \\ \frac { 1 }{ 13 }
(c) \\ \frac { 2 }{ 13 }
(d) \\ \frac { 4 }{ 13 }

Solution:

Total number of cards 52
Number of a king or a jack = 4 + 4 = 8
.’. Probability = \\ \frac { 8 }{ 52 } = \\ \frac { 2 }{ 13 } (c)

The probability that a non-leap year selected at random has 53 Sundays is.
(a) \\ \frac { 1 }{ 365 }
(b) \\ \frac { 2 }{ 365 }
(c) \\ \frac { 2 }{ 7 }
(d) \\ \frac { 1 }{ 7 }

Solution:

Number of a non-leap year 365
Number of Sundays = 53
In a leap year, there are 52 weeks or 364 days
One days is left
Now we have to find the probability of a Sunday out of remaining 1 day
∴ Probability = \\ \frac { 1 }{ 7 } (d)

A bag contains 3 red balk, 5 white balls and 7 black balls. The probability that a ball drawn from the bag at random will be neither red nor black is
(a) \\ \frac { 1 }{ 5 }
(b) \\ \frac { 1 }{ 3 }
(c) \\ \frac { 7 }{ 15 }
(d) \\ \frac { 8 }{ 1 }

Solution:

In a bag, there are
3 red balls + 5 white balls + 7 black balls
Total number of balls = 15
One ball is drawn at random which is neither
red not black
Number of outcomes = 5
Probability = \\ \frac { 5 }{ 15 } = \\ \frac { 1 }{ 3 } (b)

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