Test: Applications of Probability - Class 10 MCQ

Three face cards from spades have been removed.
Total cards=52-3=49
Total No of black face cards=3+3(3 in each spades and clubs)
Remaining black face cards=6-3=3
Probability of getting black face card=  no. of favourable outcomes/ total no. of outcomes=3/49

Total number of outcomes=90-1=89
No. of favourable outcomes = Total outcomes - One digit number =89-8=81
Probability of having a two digit number=Total number of outcomes/No. of favourable outcomes=81/89

Total no. of outcomes=52
No. of ace cards=4
No. of non-ace cards=48
Probability of getting a non-ace card = No. of favourable outcomes / total no. of outcomes
=48/52=12/13

The English alphabet consists of 26 letters, with 5 vowels (A, E, I, O, U) and 21 consonants.

• Number of consonants: 21
• Total letters in the alphabet: 26

To find the probability of selecting a consonant, use the formula:

Probability = (Number of favorable outcomes) / (Total number of outcomes)

So, the probability = 21/26.

Thus, the correct answer is:

A: 21/26

As three cards have been removed, there are now 49 cards in the deck.

As the three cards removed were the 3 spades face cards, there are only 3 black face cards left (the J, Q, K of clubs).

P ( black face card) = ( favourable outcomes ) / ( possible outcomes )

= 3 / 49

A fair dice has number 1,2,3,4,5,6 only . So there are no number greater than 6
No. of favourable outcomes=0
Total no. of outcomes=6
Probability of getting no. higher than 6=No. of favourable outcomes/Total no. of outcomes=0/6=0
 

P(E) = number of expected trials / total number of trials
A standard deck of cards has 52 cards.
Number of expected trials = 4 x 12 = 48 cards
Total number of trials = 52
Therefore, P(E) = 48/52
= 12/13

The possible outcomes when a dice is thrown = {1, 2, 3, 4, 5, 6}

Number of possible outcomes of a dice = 6

(i) Prime numbers on a dice are 2, 3, and 5.

Total prime numbers on a dice = 3

Probability of getting a prime number = 3/6 = 1/2

We have total cards = 52
4 categories=spades,clubs,diamonds and hearts
Spades and clubs are black cards
No. of favourable outcomes=13+13=26
Probability of getting a black card= no. of favourable outcomes/total no. of outcomes
=26/52=1/2

Total number of balls in the bag=9+4+7=20 balls
No. of favourable outcomes=not getting blue ball= getting either the red ball or green ball=9+7=16
Probability of not getting blue ball = no. of favourable outcomes/total number of outcomes=16/20=4/5

The possible outcomes when a dice is thrown = {1, 2, 3, 4, 5, 6}

Number of possible outcomes of a dice = 6

Prime numbers on a dice are 2, 3, and 5.

Composite numbers on dice = 4, 6

Total prime numbers on a dice = 3

Total composite numbers on a dice  = 2

So, total (prime + composite) = 5

Probability of getting a number that is either prime or composite = 5/6

There are 366 days in a leap year, i.e, 1 more than a normal year.

Now, 52 weeks make up 344 days (52 x 7 = 344)
That means that we already have 52 sundays for sure.

Then, we are left with 2 days. Now, these days can be any from a pair of- mon-tues,tues-wed,wed-thurs,thurs-fri,fri-sat,sat-sun,sun-mon. Here favourable cases are sat-sun and sun-mon i.e, 2 cases and total number of cases is 7.

So, Probability=number of favourable cases/Total number of cases.

Therefore, Probability= 2/7.