Applications of Probability - Free MCQ Practice Test with solutions,

When Harry tosses two coins simultaneously, there are four possible outcomes:

1. Heads on both coins (HH)
2. Heads on the first coin and tails on the second (HT)
3. Tails on the first coin and heads on the second (TH)
4. Tails on both coins (TT)

To calculate the probability of getting at least one head, we need to find the probability of all outcomes that have at least one head (i.e., exclude the outcome where there are no heads, which is TT).

The favorable outcomes are:

• HH
• HT
• TH

There are 3 favorable outcomes out of the 4 possible outcomes.

Thus, the probability of getting at least one head is:

P(at least one head)=3/4 

Therefore, the correct answer is b) 3/4.

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

Explanation: Total number of balls = 3 white + 5 red = 8 balls.

The number of red balls = 5.

Probability = (Number of red balls) / (Total number of balls) = 5/8.

So, the correct answer is Option D.

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

Explanation: When two coins are tossed, the possible outcomes are:

1. Head, Head (HH)
2. Head, Tail (HT)
3. Tail, Head (TH)
4. Tail, Tail (TT)

The event "at least one head" includes the outcomes HH, HT, and TH. So, there are 3 favorable outcomes.

Total number of outcomes = 4 (HH, HT, TH, TT).

Probability = (Number of favorable outcomes) / (Total number of outcomes) = 3/4.

Answer: Option B (2/3)

Explanation: The possible outcomes when a die is thrown are 1, 2, 3, 4, 5, and 6.

The numbers less than 5 are 1, 2, 3, and 4. So, there are 4 favorable outcomes.

Total number of outcomes = 6.

Probability = (Number of favorable outcomes) / (Total number of outcomes) = 4/6 = 2/3.

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
 

A standard deck has 52 cards and contains 4 aces.

The probability of winning by drawing an ace is 4 divided by 52, which equals 1/13.

Therefore, the probability of losing (not drawing an ace) is calculated by subtracting the number of aces from the total cards: (52 minus 4) divided by 52, which simplifies to 48/52 or 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

Explanation: In a deck of 52 cards, there are 3 face cards (Jack, Queen, King) in each of the 4 suits (hearts, diamonds, clubs, spades).

So, the total number of face cards = 3 face cards × 4 suits = 12 face cards.

Total number of cards = 52.

Probability = (Number of face cards) / (Total number of cards) = 12/52 = 3/13.

So, the correct answer is Option D.

Explanation: A standard deck of 52 cards contains 26 black cards (13 spades and 13 clubs).

The total number of cards = 52.

The number of black cards = 26.

Probability = (Number of black cards) / (Total number of cards) = 26/52 = 1/2.

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.